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Full text of "Search for correlated radio and optical events in long-term studies of extragalactic sources"

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SEARCH FOR CORRELATED RADIO AND OPTICAL EVENTS 
IN LONG-TERM STUDIES OF EXTRAGALACTIC SOURCES 



by 
RICIiARD BRYAJ^I POMPHREY 



A DISSERTATION PRESENTED TO THE GRADUATE COU'NCIL OF 
THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLl-IENT 
OF THE REQUIREMENTS FOR THE DEGREE OF 
DOCTOR OF PHILOSOPHY 



LTn^IVERSITY of FLORIDA 
1977 , , 



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ACKNOWLEDGEMENTS 

I wish to express my appreciation to my committee chairman, 
Dr. A. G. Sm.ith, not only for his assistance, but in particular for his 
support and direction when the future was uncertain; to my committee 
co-chairman, Dr, C. N. Olsson, for being a true friend who said things 
that needed to be said, and for his support and advice through both 
favorable and adverse situations. I also wish to thank Drs. T. L. Bailey, 
G. R. Lebo, and S. T. Gottesman for their assistance and contributions 
to my research experience. 

The study documented in this dissertation makes use of data from 
many observatories. I am indebted to Drs. J. M. MacLeod, G. A. Har'/ey, 
and B, H. Andrew of the Algonquin Radio Observatory, and to Drs. K. ?, 
Tritton, M, V. Penston, and R. A. Selmes of the Royal Greenwich Observa- 
tory for permitting me to make extensive use of their previously unpub- 
lished data. The Rosemary Hill observations were made by Drs. A. G. Smith, 
G. H. Folsom, K, R. Hackney, R. L. Hackney, R. J. Leacock, B. Q. McGimsey, 
and R. L. Scott, and by J . T. Pollock and Patricia Edwards. In addition 
Dr. J. D. G. Rather graciously made his data bank available while it was 
still in preparation. 

Much of the initial analysis was supported by a Research Corporation 

grant and was carried out at the Electronics Research Laboratory of The 

Aerospace Corporation. Ifnile there I received the generous assistance of 

)\ manv of the staff to whom I am grateful: G. G. Berry, H. Dyson, 

I 

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Dr. E. E. Epstein, W. A. Johnson, H. E. King, J. W. Montgomer}-, T. T. 
Mori, Dr. J. Mottmann, now at the California Polytechnic Institute at 
San Luis Obispo, Ms. J. D. White, and Dr. W. J. Wilson, now at the 
Uhiverity of Texas at Austin. In addition, Mrs. Suzanne Hansen typed 
much of the manuscript and J. Petersen assisted in the preparation of the 
illustrations . 

During my graduate career, I have been supported by the Research 
Corporation grant, a University of Florida Graduate School research assis- 
tantship, a University of Florida teaching assistantship, part-time 
emplojTnent at The Aerospace Corporation, and full-time employment at the 
Jet Propulsion Laboratory. I am grateful to D. J. Lynn, R. M. Ruiz, and 
Dr. D. A. Elliott of JPL for their support, patience, and understanding 
while I was finishing this work. The analysis was also aided by funds 
from the Northeast Regional Data Center of the State University System 
of Florida. 

I also wish to thank Dr. W. G. Fogarty of Universidade Mackenzie, 
Dr. J. T. McClave of the Department of Statistics and Dr. M. A. Lynch of 
the Department of Physics and Astronomy, University of Florida, for help- 
ful discussions; and W. W. Richardson and H. W. Schrader of the University 
of Florida for extensive technical assistance. 

Annual Reviews of Astronomy and Astrophysics, Springer-Verlag New 
York, Reviews of Modern Physics, The Astronomical Journal and The Astro- 
physical Journal generously granted permission to reproduce illustrations 
from their publications. The Astrophysical Journal required that the 
identical copyright notice as it appears in the Journal be included in 
the manuscript. This copyright notice follows: 



Xll 



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So that the author and publisher may be protected from the 
consequences of unauthorized use of the contents of the 
manuscript, we consider it essential to secure a copyright. 
Therefore, it is mutually agreed that upon the acceptance 
of the submitted manuscript for publication by this Journal , 
the author grants and assigns exclusively to the American 
Astronomical Society for its use any and all rights of what- 
soever kind or nature now or hereafter protected by the Copy- 
right Laws (common or statutory) of the United States and 
all foreign countries in all languages, including all sub- 
sidiary rights. The American Astronomical Society, in turn, 
grants to the author the right of republication without 
charge in any book or periodical of which he is an author, 
contributing author, or editor, subject only to his giving 
proper credit in the book or periodical to the original 
Journal publication of the paper by The University of Chicago 
Press for the American A.stronomical Society. 



I am indebted to many friends for their help throughout my graduate 
work. The assistance and companionship of Dr. James R. Kennedy and Jack 
G. Schudel, III were invaluable in the completion of a major portion of 
this work. Long discussions with Jim Kennedy helped formulate the direc- 
tion I have taken in this research; the subroutine PPLOT which appears in 
the Appendix is his, while the subroutine CORREL incorporates many of his 
ideas. Jack Schudel assisted significantly in the computations and a 
number of the illustrations. I also wish to thank Dr. Carl Olsson's 
family, John Young, Eric Van Horn, Al and Isa Adams, Jim and Jerry Hatch, 
and Jim and Barb Thieman for their help, support, and friendship. 

There are some individuals who have had a significant influence on 
my attitudes and my work during my graduate career. I wish to express 
my sincere gratitude to Ray and Andy Bloomer, Kit Harvel, Jim and Cathy 
Kennedy, and Joe and Liz Mullen not only for their support and direction, 
but also for helping me learn hoxj to play the game. 

In addition I wish to gratefully acknowledge my brother and his 
family, and the countless relatives and friends of my family who, 



IV 



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while not able to assist me directly, expressed their concern and support 
verbally and in prayer. 

Finally, I dedicate this work to Dr. George Horvat and to my parents 
for their prayers and support, both that which I am aware of and that 
which I have not even recognized. 



V 



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TABLE OF CONTENTS 

Page 

ACKNOWLEDGEMENTS ii 

LIST OF TABLES . ix 

LIST OF FIGURES x 

ABSTRACT xiv 

CHAPTER 

I INTRODUCTION 1 

Extragalactic Variables 3 

State of Our Knowledge 5 

II THEORY APPLIED TO SPECTRAL ENERGY DISTRIBUTIONS . . 10 

Spectral Energy Distributions 10 

Radio Frequency Spectra 12 

Radiation From a Single Electron 14 

Radiation From a Distribution of Electrons . . 18 

Time Variations 23 

Expanding Source Model 24 

Expanding Source Model Difficulties and 

Alternatives 27 

Inverse Compton Scattering 29 

Optical Spectra 36 

Galactic Infrared Radiation 55 

Extragalactic Infrared Radiation ..... 61 



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Page 

III ANALYSIS OF THE LONG-TERM OPTICAL AJSID RADIO RECORDS. 65 

The Research Problem 65 

The Radio and Optical Data Records .... 66 

Cross-Correlation Analysis 68 

Choice of Correlation Parameters 72 

IV ■ RESULTS OF THE CORRELATION ANALYSIS 74 

OJ 287 76 

3G 454.3 80 

BL Lac . . 98 

CTA 26 (PKS 0336-01) 102 

PKS 0405-12 102 

PKS 0420-01 108 

3C 120 108 

NRAO 190 (PKS 0440-00) 118 

PKS 0458-02 118 

3C 138 (PKS 0518+16) . 124 

PKS 0735+17 128 

PKS 0736+01 135 

01 363 135 

OK 290 143 

3C 273 147 

PKS 1354+19 153 

Oq 208 . . 161 

PKS 1510-08 161 

NRAO 512 161 



VI 1 



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Page 

3C 371 158 

3C 446 176 

PKS 2345-16 176 

Summary 186 

V CONCLUSIONS 191 

Spectral Energy Distributions 191 

Lack of Correlation 197 

OJ 287, BL Lac, and 3C 454.3 199 

Implications of Correlation 204 

Further Work 207 

APPENDIX 

I COMPUTER PROGRAMS USED IN THE STATISTICAL ANALYSIS . 210 

II FURTHER USE OF COMPUTER PROGRAMS AND DATA BANK . . 236 

BIBLIOGRAPHY 238 

BIOGRAPHICAL SKETCH .... 243 



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LIST OF TABLES 

TABLE Page 

1 INTERCOMPARISON OF WAVELENGTHS WITH FREQUENCIES . . 9 

2 ' RANGE OF ELECTRON ENERGIES FOR A GI\^N POI^JER LAW 

INDEX - 20 

3 LACERTID OPTICAL AND NEAR-IR SPECTRAL INDICES . . 39 

4 STOIMARY OF RESULTS OF THE LINEAR CROSS -CORRELATION 
ANALYSIS 75 

5 SUMMARY OF CORRELATION ANALYSIS RELATIVE TO OPTICAL 

AND RADIO VARIABILITY Su-BCLASSES 187 

6 RADIO AND OPTICAL AMPLITUDES FOR OJ 287 FLARE . . 203 

7 RADIO AND OPTICAL AMPLITUDES FOR BL Lac FLAP.E . . 204 

8 RADIO AND OPTICAL AMPLITLT3ES FOR 3C 454.3 FLARE • . 204 
A-1 DATA BANK FORMAT 236 



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LIST OF FIGURES 



Figure Page 

1 Spectral Energy Distributions for Five Quasi-Stellar 
Objects and the Seyfert Galaxy NGC 1068 .... 11 

2 Four Classes of Radio Frequency Spectra .... 13 

3 Synchrotron Spectrum from a Single Electron as a 

Function ofx = v/v 16 

c 

4 Expected Synchrotron and Inverse Compton Spectra 

for the Galactic Halo 34 

5 30 120. Optical and Near-Infrared Spectrum ... 38 

6 3L Lac. Optical and Near-Infrared Spectrum ... 40 

7 OJ 287. Optical Spectrum 41 

8 OJ 28 7. Optical and Near-Infrared Spectrum 
Extrapolated to Short Radio Wavelengths .... 43 

9 BL Lac. Changes in Optical and Near-Infrared 

Spectrum with Time 45 

10 Selected Quasars. Optical and Near-Infrared Spectra 47 

11 Selected Quasars. Optical and Near-Infrared Spectra 49 

12 Selected Quasars. Optical and Near-Infrared Spectra 51 

13 3C 345, 3C 446, 3C 454.3. Changes in Optical 

Spectral Index with Time 52 



14 Spectral Energy Distributions Showing Known Infrared 
Components 



57 



15 Schematic Extinction Curve . 58 

16 OJ 287. Optical and Radio Curves 7 7 

17 OJ 287. R vs At for all Data 78 

18 OJ 287. Radio Flux vs Optical Magnitude .... 79 



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Figure Page 

19 OJ 287, Part I. R vs At 81 

20 OJ 287, Part II. R vs At 82 

21 OJ 287, Part I. Radio Flux vs Optical Magnitude. . 83 

22 OJ 287, Part II. Radio Flux vs Optical Magnitude . 84 

23 3C 454.3. Three Independent Optical Data Records . 86 

24 3C 454.3. Optical and Radio Curves 88 

25 3C 454.3. R vs At for all Data 90 

26 3C 454.3. R vs At for Part of Optical Data ... 91 

27 3C 454.3. Radio Flux vs Optical Magnitude. ... 92 

28 3C 454.3. Radio Flux vs Optical Magnitude. ... 93 

29 3C 454.3. R vs At for Part of Radio Data .... 95 

30 3C 454.3. Tim Independent Radio Data Records. . . 96 

31 3C 454.3. R vs At for I\vo Radio Records .... 97 

32 BL Lac. Optical and Radio Curves 99 

33 BL Lac. R vs At for all Data . • 100 

34 BL Lac. R vs At for all Data 101 

35 CTA 26. Optical and Radio Curves 103 

36 CTA 26. R vs At for all Data 104 

37 CTA 26. Radio Flux vs Optical Magnitude .... 105 

38 CTA 26, Radio Flux vs Optical Magnitude .... 106 

39 PKS 0405-12. Optical and Radio Curves 107 

40 PKS 0405-12. R vs At for all Data 109 

41 PKS 0420-01. Optical and Radio Curves Ill 

42 PKS 0420-01. R vs At for Part of Radio Data ... 112 

43 PKS 0420-01, R vs At for all Data 113 

44 3C 120. Optical and Radio Curves 115 



XI 



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Figure Page 

45 3C 120. R vs At for all Data 117 

A6 NRAO 190. Optical and Radio Curves . . . .' . . 119 

47 NRAO 190. R vs At for Part of Radio Data .... 120 

48 NRAO 190. R vs At for all Data 121 

49 PKS 0458-02. Optical and Radio Curves 122 

50 PKS 0458-02. R vs At for all Data 123 

51 3C IBS. Optical and Radio Curves 125 

52 3C 138. R vs At for all Data 127 

53 PKS 0735+17. l\-70 Independent Radio Data Records. . 129 

54 PKS 0735+17. R vs At for Two Radio Records ... 130 

55 PKS 0735+17. Optical and Radio Curves 131 

56 PKS 0735+17. R vs At for Part of Radio Data ... 132 

57 PKS 0735+17. R vs At for Part of Radio Data ... 133 

58 PKS 0735+17. R vs At for all Data 134 

59 PKS 0735+17. Radio Flux vs Optical Magnitude. . . 136 

60 PKS 0735+17. Radio Flux vs Optical Magnitude. . . 137 

61 PKS 0736+01. Optical and Radio Curves 139 

62 PKS 0736+01. R vs At for Part of Radio Data ... 140 

63 PKS 0736+01. R vs At for all Data 141 

64 01 363. Optical and Radio Curves 142 

65 01 363. R vs At for all Data 144 

66 OK 290. Optical and Radio Curves 145 

67 OK 290. R vs At for all Data 146 

68 3C 273. Two Independent Radio Data Records . . . 148 

69 3C 273. R vs At for Two Radio Records 150 

70 3C 273. Optical and Radio Curves 152 



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Figure Page 

71 3C 273. R vs At for Part of Radio Data 154 

72 3C 273. R vs At for Part of Radio Data 155 

73 3C 273. R vs At for all Data I57 

74 PKS 1354+19. Optical and Radio Curves 158 

75 PKS 1354+19. R vs At for all Data 160 

76 OQ 208. Optical and Radio Curves 162 

77 OQ 208. R vs At for all Data 163 

78 PKS 1510-08. Optical and Radio Curves 164 

79 PKS 1510-08. R vs At for all Data 165 

80 NRAO 512, Optical and Radio Curves 167 

81 NRAO 512. R vs At for all Data 170 

82 NRAO 512. R vs At for Part of Optical Data . . . 172 

83 3C 371. Optical and Radio Cun/es 174 

84 3C 371, R vs At for all Data I75 

85 3C 446. Two Independent Radio Data P.ecords . . . 177 

86 3C 446. R vs At for Two Radio Records 179 

87 3C 446. Optical and Radio Curves 181 

88 3C 446. R vs At for all Data 182 

89 PKS 2345-16. Optical and Radio Curves 133 

90 PKS 2345-16. R vs At for all Data 185 

91 Radio and Infrared Spectra of Selected Extragalactic 
Sources . 193 

92 Idealized Spectrum of an Extragalactic Variable . . 194 

93 OJ 287. Monthly Mean Fluxes at Different 

Wavelengths 201 



XI 11 



II II I I 'I I I II "I iir ■ii>'ii inriT - 'm i .■ ijftt ^Mww_^wy<wii|i_jiii] ^^t 



Abstract of Dissertation Presented to the Graduate 
Cotmcil of the University of Florida in Partial Fulfillment 
of the Requirements for the Degree of Doctor of Philosophy 



SEARCH FOR CORRELATED RAJDIO MT> OPTICAL EVENTS 
IN LONG-TERM STUDIES OF EXTRAGALACTIC SOURCES 



By 

Richard Bryan Pomphrey 
March, 1977 

Chairman: Dr. Alex G. Smith 
Major Department: Astronomy 

Much of the research on extragalactic variables has attempted to 
determine the radiation mechanisms that cause the observed spectral 
energy distributions. This knowledge in turn should help to define the 
source of energy in these variable objects. 

This work documents the first attempt to assemble the long-term 
records of optical and radio fluxes of a large sample of variable extra- 
galactic sources in a search for correlated radio and optical events, 
using a linear cross-correlation analysis to reinforce visual comparisons. 
The results of such research may help to parameterize either the radiation 
mechanism involved or the source structure which can then be used in the 
study of the radiation mechanism. 

Chapter I presents the general background of this research topic, 
including the definitions of quasi-stellar objects, Seyfert galaxies, 

xiv 



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N galaxies, and Lacertids, and the similarities among these objects which 
are used as the justification for studying these objects as different 
manifestations of some common basic phenomenon. Soth Chapters I and II 
address Xvhat is presently known, hypothesized, or speculated about these 
variables . 

Chapter II gives a brief but extensive overview of the theoretical 
considerations involved in research on variable extragalactic objects as 
a reference against which the results of the search for correlations can 
be studied. This chapter includes reviews of the character of the radio, 
infrared, and optical spectra, their changes with time and possible 
causes, with special emphasis on the synchrotron and inverse Compton 
mechanism.s and the expanding source model. 

A simple method of synthesizing evenly spaced time series by 
stepping through the data in given increments of time is discussed in 
Chapter III, along with the method used to linearly/ cross-correlate 
optical magnitudes with radio fluxes and the problems of this approach. 

A relatively complete documentation of the long-term optical and 
radio variations is presented graphicall:/ in Chapter IV, where optical 
data from the Rosemary Kill, Royal Greenwich, Yale, and Goethe Link 
Observatories has been combined with radio data from Algonquin Observatory 
and the University of Massachusetts. The results of the correlation 
analysis are presented through discussion and extensive linear correla- 
tion and regression plots, which document a significant correlation for 
OJ 287 and a potential correlation for 3C 454.3. 

The lack of correlation in most of the sources studied allows a 
decrease in the energy requirements of events in these sources and 
carries implications for the source structure, vjhich are discussed in 
Chapter V. 

XV 



The possible implications of the correlation for OJ 287 are reviewed, but 
no fir:n conclusions concerning source structure or radiation mechanism 
can be drawn without further data. Finally, extensions of the investiga- 
tion begun in this work are suggested. 

A sunimary of the correlation analysis results is reported in a paper 
by R. B. Pomphrey, A. G. Smith, R. J. Leacock, C. N. Olsson, R. L. Scott, 
J. T, Pollock, Patricia Edwards, and W. A. Dent, "A Search for Correlated 
Radio and Optical Events in Long-Term Studies of Extragalactic Sources", 
in The Astronomical Journal , 81, 489, (1976), 



XVI 



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CHAPTER I 
INTRODUCTION 



In the early 1960 's, the discovery that quasi-stellar objects were 
a unique source of radiation initiated a period of intense observational 
and theoretical research which still continues. Although a great deal 
of data has helped define these objects phenomenologically, we are still 
not able satisfactorily to explain them theoretically. Moreover, the 
search for OSO's has revealed that there are many classes of sources 
which are quite similar to quasars: Seyfert, N-type, and compact 
galaxies, and Lacertids. 

In this work I will use the term quasi-stellar object (Q30 or 
quasar) to refer to all objects variously called quasi-stellar radio 
sources or quasi-stellar sources whether or not they are radio emitters. 
Tnese objects possess the following general characteristics: a) faint, 
star-like appearance on a photographic plate; b) an excess of ultra- 
violet and infrared radiation (relative to stellar spectra) ; c) broad 

o 

emission lines (widths of up to 100 A) x^rith absorption lines sometimes 
present; d) optical spectra exhibiting large emission line redshifts 
[0.06 $ z ^ 3.53, where z = (,\ - Xo) / Ao]. Some quasars exhibit multiple 
absorption redshifts while a few have m.ultiple emission redshifts. If 
the spectral redshifts are assumed to be cosmological, they indicate 
objects which are receding from, us at a significant fraction of the 
speed of light, up to 0.91c for OQ 172 (z = 3.53). There has been some 
discussion (Chiu et al . 1973) concerning the creation of two classes of 



quasars, one of which would be used to explain the Lacertid phenomenon. 

Seyfert, N-type, and compact galaxies are often grouped together 
because they all possess certain characteristics in common, and depending 
on who is classifying them, the defining criteria are not always 
mutually exclusive. Morgan (1972) presents an extensive summary of 
classification criteria. 

Seyfert galaxies are generally characterized by small, intensely 
bright nuclei (described as stellar in visual appearance) in which 
violent activity appears to take place, manifesting itself in broad 
hydrogen emission lines charactized by Doppler velocity widths of a few 
thousand km/s; and by an excess of ultraviolet and infrared radiation. 
14any Seyfert galaxies are spirals and some exhibit forbidden emission 
lines which are much narrower than the broad lines and are not normally 
seen in galactic spectra. 

N and compact galaxies basically are classifications of form and 
are thus somewhat a function of the distance and observing instrument. 
An N galaxy is defined as one having a small, brilliant nucleus contain- 
ing a considerable fraction of the total luminosity, superimposed on a 
much fainter main body. A compact gala^cy exhibits .high surface bright- 
ness and is only partially resolved on a medium to high resolution 
photographic plate. 

BL Lac is the defining source for the Lacertid class of objects, 
which exhibit (Strittmatter _et al. 1972) a) rapid intensity variations 
in the radio, infrared, and optical, lasting days to xjeeks; b) an 
energy distribution which indicates most of the energy is emitted at 
infrared wavelengths; c) an absence of emission lines, and in many 
cases an absence of absorption lines; d) a strong and rapidly varying 



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polarization; e) in some cases a stellar appearance (OJ 287) while in 
other cases a non-stellar appearance (BL Lac) . 

In general, N galaxies have been regarded as intermediate in form 
and luminosity between quasars and Seyfert galaxies. 

Extragalactic Variables 

As early as 1963, Burbidge et_ _al. suggested a possible relation- 
ship between quasars and Seyfert galaxies; Sandage (1970) and Kristian 
(1973) have provided evidence that quasars are like N-type galaxies. 

For the purposes of this study, the most important point is that 
many quasars, Seyfert and N-type galaxies, and Lacertids are strong radio 
emitters and exhibit intensity variations in both optical and radio 
emission. Moreover, apart from differences in absolute luminosity, these 
classes of objects are generally indistinguishable on the basis of their 
radio spectra or their time variations (Kellermann and Pauliny-Toth 1968) . 

Because real differences appear to exist among the optical classi- 
fications, I will generally note the specific type of object being 
discussed at any point. However, because of the increasing circumstantial 
evidence that there is a relationship among all these variable sources 
with respect to the nature of the radiation mechanism and energy source 
active in each of them, unless othertNTise noted I will treat all these 
classes of objects as somewhat different manifestations of the same basic 
phenomena, and refer to all members of this general class as Extra- 
galactic Variables (EGV) . 

Why are EGV's such an intriguing area of research? Stated simply, 
they emit far too much energy in too little time from too small a volume 
to be completely explained by any present theories. If they are at 



45 
cosmclogical distances, quasars have optxcal lumxnosities of xO to 

46 ^^3 45 , , 

10 ergs/sec and radio luminosities of 10 to 10 ergs/sec (Burbidge 

and Burbidge 1967) . 

The optical intensity of many quasars varies on a time scale which 
is characteristically on the order of a tenth of a year, which implies 
that the active region of the quasar must be very compact. If we make 
the assumption that we can use the Hubble expansion constant to determine 
the distance of the quasars from their redshift, then we are confronted 
with a m.ajor scientific problem. Although not theoretically impossible, 
we are considering the largest masses ever seen in such small volumes, 
10 to 10 ~ solar masses in a spherical volume roughly one tenth of a 
light year in diameter (Morrison 19 73). Making long lasting stable 
models for such massive and compact systems, and developing highly 
efficient mechanisms for converting rest mass into radiation energy 
remain among the most perplexing problems associated with quasars. 

From another perspective, beyond the basic phenomena used to 
classify the types of EGV's, one almost immediately enters a labyrinth 
of controversial if not contradictory observations, explanations, hypoth- 
eses, interpretations, and plain speculations which are fed by generally 
commendable attempts to bring some meaning to this intriguing area of 
research by using the best data available, which regrettably often suffer 
from inadequate time or spatial resolution or inadequate signal to noise 
ratios. It seems that as researchers make every effort to increase time 
and spatial resolution, there often is that much more structure to be 
found, structure which is changing! In addition these research efforts 
follow on the heels of, and in fact act as significant motivation for, 
better receiving systems all the way from centimeter to X-ray wavelengths, 



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Thus whatever I present in this study does not represent incontro- 
vertible truth, but rather that which appears to be most generally- 
accepted by its frequency in the literature and which seems reasonable 
to me. It also represents the most successful effort to date to analyze 
the available variability data. 



State of our Knowledge 



Some of the most basic questions which remain unresolved are the 
following: a) Are these objects at the cosmclogical distances indicated 
by the redshift of their spectra, or are they in fact much closer? 
b) IJhat is the source of energy emitted, which in some cases is awesome 
even if the source is not at a cosmclogical distance? c) How is the 
energy converted into radiation? d) What kind of radiation is emitted? 
Because the radiation emission is what we obser^/e, hopefully by answering 
(d) we can make progress on the other basic questions. In this work, 
where necessary, I will assume the extragalactic variables are at cosmol- 
ogical distances. I will not address the question of energy source and 
energy conversion other than to note that the most popular theories 
(Kellermann 1974) involve the collisions of stars or galaxies; the 
collapse of stars, superstars, galaxies, or intergalactic matter; the 
explosion of stars, superstars, or galaxies, including chain reactions; 
positron-electron annihilation and creation of matter; quark inter- 
actions; and a pulsar-like mechanism referred to as the "spinar" model. 
What then do we know from the observations of extragalactic variables? 
a) Ver^' Long Baseline Interf erometry measurements indicate that 
the variable sources often have multiple, compact components, 
typically on the order of 1.0 to 0.001 arc seconds; the physical 



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dimensions deduced from these measurements are a function of dis- 
tance and expansion velocity of the source. In weak radio 
galaxies which have nuclear structure apparently' identical to 
quasars, the radio emission is concentrated in a very small region 
near the nucleus, with dimensions ranging from 100 pc to less than 
0.1 pc. 

b) Radio and optical variations on time scales of a day to a 
few years have been observed in different sources. Assuming an 
event cannot occur in a time much shorter than the light travel 
time across the active region, the duration gives an estimate of 
the size of the active region which is independent of the distance 
to the source, but dependent on whether or not a relativistic 
expansion is taking place. It is possible that the source of 
energy could be much larger than the active region if there exists 
some energy coupling or transfer mechanism. 

c) Tnere are at least two observations at optical frequencies 
that provide evidence for solid material in or at least near the 
nuclei of Seyfert galaxies and quasars (Burbidge and Stein 1970) . 

d) Based on observations of variable nuclei, Burbidge (1970) has 
speculated that activity in galactic nuclei is a widespread and 
probably quite general phenomenon, taking place in many if not 
all types of galaxies. In general there is a wide range of power 
levels observed and activity has been seen over the full range of 
distance from nearby galaxies to the most distant objects observed. 
Thus considering light travel time, this activity has been 
observed over the full range of observed time. This has been rein- 
forced by a recent discovery by Crane et al. (1976) of centimeter 



variations from the nucleus of M81, a nearby spiral galaxy. 

e) A strong correlation exists between high optical polarization 

and variability. 

The radio, optical, and infrared data collected on EGV's all seem 
to indicate a high probability that what we are observing are different 
manifestations of some basic phenomenon common to all EGV's and very 
likely common also to our own galaxy. 

""he obvious question, then, is just what is the basic phenomenon? 
This question has refused to yield to almost 13 years of concerted 
effort, for the answer is anything but obvious. 

To begin with, we don't even know what the basic phenomenon is for 
which we are looking. Most likely it is either a common energy source, 
or a common mechanism which couples the energy generated to the energy 
emitted. This then is probably comouflaged by the magnitude of gener- 
ated energy, the characteristics of the material surrounding the gener- 
ator, and the number of such generators in a limited region of space. 

If a basic phenomenon exists in all EGV's, then theories which 
attempt to address themselves to the phenomenon must be applicable in 
all cases; however, because of the many differences among observed EGV 
parameters, any theory which is not applicable to all EGV's is not 
necessarily completely invalid. It may simply be valid for certain 
conditions found in only som.e of the EGV's, and may require further 
refinement to apply more generally. 

Our approach then must also be basic; what can we observe? 
Because we are searching for something common to all these variables, 
what relationships can we find among the varied observations; and 
finally, •what do these relationships tell us, if anything? This then 



is the basic approach used in carrying out the research described herein. 

Analysis of intensity variations may provide critical data on the 
radiation mechanisms involved, their relationship to one another, 
distribution of radiation energy, and possible source structure. This 
is particularly true if a correlation between activity at different 
wavelengths can be established and will become clearer after reviewing 
the character of the spectral energy distributions of the variable 
sources, and the attempts made thus far to explain them theoretically. 

For the study and intercomparision of radio, infrared, and optical 
data which follows, the use of Table 1 is indispensable. The entries 

o o o 

for 3575 A, 4400 A, and 5490 A correspond to Johnson m^ , m , and m^ 
respectively, before correction for atmospheric extinction. 



TABLE 1 
INTERCOMI^imiSON OF WAVELENGTHS WITH FREQUENCIES 



(y) 



WAVELENGTH 

O 

(A) 





INVERSE 


LOG INVERSE 






LOG 




WAVELENGTH 


WAVELENGTH 


FREQUENCY 


FREQUENCY 


(mm) 


(cm 


') 




(Hz 


) 






3.3 


X 


10^ 


4.5 


1.0 X 


< 

10^^ 


15.0 




2.7 






4.4 


8.2 X 


14.9 




2.5 






4.4 


7.5 




14.9 




2.2 






4.4 


6.8 




14.8 




1.8 






4.3 


5.4 




14.7 




1.0 




10^ 


4.0 


3.0 




14.5 




8.3 


X 


3.9 


2.5 




14.4 




6.2 






3.8 


1.9 




14.3 




4.5 






3.7 


1.4 


10^3 


14.1 




2.9 






3.5 


8.6 X 


13.9 




2,1 






3.3 


6.2 




13.8 




1.2 






3.1 


3.5 




13.5 




1.0 




10^ 


3.0 


3.0 




13.5 




5.0 


X 


2.7 


1.5 




13.2 




3.3 






2.5 


1.0 


10^2 


13.0 


0.1 


1.0 




10-^ 


2.0 


3.0 X 


12.5 




3.3 


X 


1.5 


1.0 


^^10 


12.0 


1.0 


1.0 




10« 


1.0 


3.0 X 


11 . 5 


3.3 


3.0 


X 


0.5 


9.1 X 


11.0 


9.0 


1.1 






0,4 


3.3 




10.5 


10.0 


1.0 






0.0 


3.0 




10.5 


28.0 










1.07 




10.0 



0.3 

0.4 

0.55 

1.0 

1.2 

1.6 

2.2 

3.5 

4.8 

8.5 

10.0 

20.0 

30.0 

100.0 

300.0 

1000.0 



3000 
3675 
4000 
4400 
5490 
10,000 



CHAPTER II 
THEORY APPLIED TO SPECTRAL ENERGY DISTRIBUTIONS 



Spectral Energy Distributions 

Much of the theoretical effort expended on EGV's and also on non- 
variable quasars has been devoted to attempts to explain the radiation 
mechanisms which give rise to the spectral energy distributions of these 
sources. Knowledge of the radiation mechanisms, the parameters control- 
ling these mechanisms, and the possible relationships between mechanisms 
(if more than one is responsible) will provide the information necessary 
to help explain the energy source and coupling mechanisms . A number of 
characteristic energy distributions are portrayed in Figure 1 
(Neugebauer et_ al. 1971 and Telesco ^ al . 1976) where the log flux 
density (with vertical offset C) vs the log rest frequency have been 
plotted for the quasars 3C 273 (C = 31.0), 3C 445 (C = 31.0), 3C 48 
(C = 30.0), 4C 29.68 (C = 30.0), 3C 249.1 (C = 29.0), and the Seyfert 
galaxy NGG 1068 (C = 33.0). The dashed lines simply connect observed 
portions of the spectra; thus they extend across most of the infrared 
portion of the spectrum where little data has been collected due to the 
lack of atm.ospheric observing windows at most of these frequencies. 

Subsequent data in the near and far infrared now indicate that 
there are probably two basic types of spectra, one which shows a large 
increase in the infrared spectrum, as in NGC 1068, and another which 
follows the dotted line for 3C 273 to within the accuracy of measure- 
ment (Simon 1976). Quasars and Seyfert galaxies exhibit both types of 

10 



— •vw!r*'.«£>,^-_;>_ 



11 



NGC1068 




^-.\ 









10 



11 



12 
Log v^iHi) 





13 



14 



15 



16 



Figure 1. Log flux density (with zero-level offsets) vs log rest fre- 
quency for the quasars 3C 273, 3C 446, 3C 48, 4C 29.58, and 3C 249.1. 
Reproduced from Neugebauer _e^ _al. (1971) with permission of the authors 
and the Annual Review of Astronomy and Astrophysics. More recent 
data obtained from Telesco e_t ad^. (1976) and Rieke and Low (1975) x\rere 
used to plot the curve for the Seyfert galaxy NGC 1068. 



rm ig j i —iJgcCigBg 



12 



spectra. In addition, there is now evidence of a possible near-infrared 
"dust bump" in the energy distribution of a number of quasi-stellar 
objects (Becklin 19 76). The bump may be described as a small departure 
from the otherwise smooth spectra, as opposed to the large infrared 
contribution in the spectra of NGC 1068. 

In general, the known spectral energy distributions for any source 

can be divided into three regions whose boundaries overlap. The radio 

11 
spectrum extends from about 1 mm (3 x 10 Hz) to all longer wavelengths, 

14 
The infrared spectrum extends from about 0.7 y (10 Hz) to about 1 mm; 

o 

and the optical spectrum encompasses the region from about 3000 A 
(-10"^^ Hz) to 7000 A. 



Radio Frequency Spectra 
With respect to radio spectra, magnetic field strength, or time 
scale of flux density variations, no distinction can be m.ade between 
quasars and compact radio galaxies (Kellermann and Pauliny-Toth 1969) ; 
thus they are grouped together in this section. A detailed study 
indicates three basic types of radio spectra (Kellermann 1974) : 

a) Straight (Class S) spectra, where the flux density decreases 
monotonically over the whole range of observed frequencies, as in 
Figure 2d; 

b) Curved (Class C) spectra, which are steeper at shorter wave- 
lengths (C-) as in Figure 2c, or have a sharp cut-off at shorter 

wavelengths (C ) as in Figure 2b; 
° max 

c) Complex (CPX) spectra, which have one or more maxima or minima 



100 



10 



\ 

\ 

4 C 39.25 ♦., 
QSS 



(al 



10 



(.0 



102 103 



10 



104 



1000 


♦ , 


1 












100 




•N 












10 




3C 1 23 \ 








(jalaxy 


\ 


1 


(c 







105 



102 103 ,0'' 105 



100 



10 



1934-63 
galaxy 



lOOOr 



100 



10 



3C 2 
QSS 



1' 
10 



(d) 



(I') 



(ta> 

1. 

10 102 103 



(ci; 



10^ 10^ 



102 103 io4 105 



Figure 2. il 1 us tr;i L i on of three basic grou])s of radio fracjucney specLra: (a) ^iC 39.2'), Class CPX 
(Comi'.lox) ; (h) IV'i^i-b'i, CMas.s C max (Ciirvuil) ; (c) 'Ul 123, Class C (Curved); (d) 3C 2, Cla-'-.s S (Slrai s;h t) 

Koriroduced from Calacilc and Kxtjagalact; i(-,__Radio Asl.ronomy, edited Iv/ C. L. Verscliuur and K. I. Ke 1 1 enuaiin 

(ii. iJZ) . Copyrigllt L97A hy Si)rin}',er-Verl.ag New York, Inc. Used wilh (leriii issloii of ])uh] i ::>\iva: and ed i I Drs . 



w 



•^^ni^^Bsg-ff^HiiiF^' -T^ e' r- yg »iwrfc 



14 



It is generally accepted that magnetic fields and a flux of high 
energy relativistic electrons exist in the EGV's. From such physical 
conditions, energy may be emitted by electrostatic bremsstrahlung 
scattered from plasma waves, s3mchrotron radiation, inverse Compton 
scattering, or by plasma shock waves if the source is turbulent. I-Ihile 
there are other possibilities, these are most often discussed in the 
literature. 

The good qualitative and in some cases quantitative agreement be- 
tween the synchrotron hypothesis and the observations has presently 
established this as the most likely radiation mechanism, at least at 
radio wavelengths. 



Radiation from a Single Electr on 



In the presence of a magnetic field of strength B, a non-relativ- 
istic electron will move in a helical path about a field line and emit 
radiation at a single gyro or cyclotron frequency (v ) which is given by 



v 1 eB -,, . ,^. 

V = -z-^ = ^ (Hz) (1) 

g zttR 2ii mc 



where R is the perpendicular distance of the electron from the magnetic 
field line, m is the electron rest mass, v is the electron velocity, 
e is the electron charge (emu), B is the magnetic flux density, and c is 
the velocity of light. 

Blumenthal and Gould (19 70) have shown that a relativistic electron 
spiraling in a magnetic field emits a total instantaneous power given by 



15 



/y e~ 



P(v) = 



mc 



K^^^iOd^ 



c v/v 



(2) 



where the critical frequency is expressed by 



and where 



eB 



2 \ 2iraic 



T, 



= 1.608 X lO-""-^ B eI ,, 
J- GeV 



= 4.21 B_^ y (MHz) 



(3) 



C = 



eB. 



Y mc 
r 



1-^ 



L 



-1/2 



-1/2 



= (1 - r) 



(4) 



K (C) is a modified Bessel function of the 5/3 order, E is the 
electron energy (E = v mc") , and B_^ = B sin9^ where 6^ is the pitch angle, 
the constant angle between the electron velocity and the magnetic field. 
The synchrotron spectrum from a single electron as a function of x = v/v^ 
is illustrated in Figure 3. As can be seen from equations (2) and (3), 
for a single particle emitting synchrotron radiation in a homogeneous 
magnetic field, the emission received at a particular frequency is 
directly related to the energy of the electron producing this radiation, 
and the strength of the magnetic field. 



*gM^ tj^-* i W fc O« l !- »>'^ 



16 




Figure 3. S],"nchrotron spectrum from a single electron as a function of 
X = v/v . Reproduced from Blumenthal and Gould (1970) v/ith permission 
of the authors and the Reviews of Modern Physics. 



* »l>- '- » ^ "W ^L W Mfri M WC^ wCii lUl KUa^ 



17 



The distribution P(v) has a broad peak near v '^ 0.28 v . At hio-her 

c 

frequencies (v >> V ) , the spectrum approaches 



P(v) ^i 



1/2 I e-^B. 



1 mc 



I V 



c / 



1/2 



-(v/v^) 



(5) 



While at very low frequencies (v << v ) the spectrum can be approximated 



by 



P(v) 



4iTe Bj_ 
r(^)mc^ 



V 

2v" 



^ 1/3 



(6) 



where r(l/3) is the Gamma function. P(v) varies little over a large 
range of frequencies, decreasing to half its maximum value at 
v/v^ = 0.011 and 1.47 (Oort and Walraven 1956). Most of the radiation 
is concentrated in a narrow cone, the axis of which coincides with the 
instantaneous velocity vector of the electron. The angle between the 
axis and the sides of the cone is given by 



,2 1/2 1 mc" 



(7) 



As a result the radiation is strongly polarized. In the case where the 

o 

pitch angle, 6^, is 90 , the electric vector is polarized parallel to the 
plane of the electron orbit. An observer in this plane will receive a 
pulse of radiation every time the electron completes an orbit, at 



18 



intervals t such that 



1 

Y — 
r V 



\ 



= V 



2^Tr \ 



(8) 



The duration of the pulse follows from equation (7) and is given by 



At 



9 

Y V 
r g 



(9) 



/ 



VJhile it can be seen from equations (1), (2), and (4) that the 
synchrotron spectrum is made up of discrete frequencies, the radiation 
is concentrated in the higher-order harmonics of the classical gyro- 
frequency, V , (Kellermann 1974) and thus is often considered continuous. 

6 

o 

In the case where 8 = 90 , an observer receives all the radiation 

e 

o 

emitted during the time At. For 9^ r 90 , the observed spectrum is 

-2 -1 
reduced by a factor of (sin ) , because the distance between the 

electron and the observer changes with time. However, for a distrib^ition 

of electrons, the emitted and received powers are again equal. 

Radiation from a Distribution of Electrons 
Brown (1974) , has shown that a homogeneous and isotropic ensenble 
of electrons having a number density per unit energy of N(E)dE and 
located in a vacuum in the presence of a uniform magnetic field B of 
spatial extent L, will radiate a specific intensity I(v) given by 

I(v) = ''^— ^2"^ |N(E)dE|^) / K5/3 (£)d5 (10) 



19 



where N(E)dE is the number of electrons per cm with energies in the 
inter\^al E to E + dE, If the electrons are characterized by a power law 
energy distribution between particular limits E and E^, given by 



dN(E) = N(E)dE = 



Ke"^ dE 



(E^ < E < E^) 



(11) 



then the specific intensity takes the form 



I(v) = 



e_i_L 
mc" 



A 



3e 

4T;mc 



(Y-l)/2 



a(Y)KB 



(y+l)/2 



-(Y-l)/2 



(12) 



where K is a constant, a(Y) is a slowly varying function of y and in 
general a(Y) =0.1. The specific intensity radiated will be observed as 
a brightness distribution, and the integral of this brightness distri- 
bution over the whole source yields the flux density S. Thus from 
equations (11) and (12) it can be seen that a power law distribution of 
electrons of spectral index y emits a power law photon spectrum which is 
characterized by 



S ■= V 



(13) 



w 



here the two indices are related by 



a = 



(14) 



Thus assuming that a power law electron energy distribution is the source 
of emitted radiation, the index Y can be obtained by measuring the slope 
a of the observed spectral energy distribution (Figure 1) . 



20 



The range of electron energies which contribute to synchrotron 
emission at a given frequency is strongly a function of the electron 
spectrum and thus of the index y. Table 2 (from Brown 19 74) lists the 
range of values E to E which is responsible for 90% of the emission at 
a particular frequency, for a given value of y. 

TABLE 2 
RA.NGE OF ELECTRON ENERGIES FOR A GIVEN POWER LAW INDEX 



y 1.0 1.5 2.0 2.5 3.0 4.0 5.0 

*--^2^^1^90% 1620 117 56 22 15 8.9 6.1 



Thus as y Increases, the range of electron energies increasingly narrows, 
indicating that the assumption or approximation of a power law distri- 
bution of electron energies needs to hold only over a narrow energy 
range. The shape of the electron energy distribution may deviate 
enormously from a power law outside the specified energy range without 
significantly affecting the synchrotron emission spectrum. The validit;^ 
of the assumption of a power law distribution ranges from y > 1.0 
(Kellermann 1974) to y $ 5.0 (Brown 1974). Finally, it should be noted 
from equation (5) that no form of electron energy distribution can give 

a synchrotron spectrum that rises faster than the low frequency asymp- 

1/3 
totic limit of v for a single electron. 

The straight radio frequency spectrum in Figure 2d is believed to 
result from synchrotron emission from a power law distribution of 
electrons as just discussed. Such spectra generally have indices in the 
range -1.3 < a < -0.6, with a median value of about -0.8, which corres- 
ponds to y == 2.6. Deviations from this straight spectra can arise from 



21 



numerous causes. To maintain a consistent presentation of the synchro- 
tron hypothesis, I will discuss here only gross spectral changes x-rhich 
have synchrotron-related causes, and defer discussion of other causes to 
another investigation. 

The turnover or low frequency cutoff in Figure 2b can result from 
synchrotron self -absorption. Theory predicts that as the brightness 
temperature of the source approaches the equivalent kinetic energy of 
the electrons, self-absorption will become important, and the source 
will become completely opaque at a frequency given by 



(15) 



where 9 is the angular extent of the source in arc seconds, B is in 

2 
gauss, the (1 + Z) term accounts for the effect of the redshift, (S^/8 ) 

is the surface brightness of the source, and S is the maximum flux 

density at v . 
m 

A study of the values of v vs surface brightness for sources for 
■' m 

which has been measured, shows that the observed cutoffs in the radio 
spectra can be accounted for by synchrotron self -absorption with a 
magnetic field of B = 10 " gauss. This corresponds to a maximum bright- 

■7-1 12 

ness temperature of T ~ 10 to 10* K, It is hypothesized that this 

m 




12 
brightness temperature of 10 K corresponds to the case where energy 

loss by synchrotron radiation is just equal to the energy loss caused by 

inverse Compton scattering. According to this hypothesis, inverse 

Compton scattering would cause a rapid "cooling" of a source which has a 

l'^ 
T = 10 K. 
m 



22 



According to synchrotron theory, as v (< v^) increases, one 

receives more radiation from deeper in the source and the fl-oic increases 

until V = V , at which point the source becomes optically thin and the 
m 

flux received becomes a function of the electron energy distribution as 
in Figure 2d. For frequencies \) < v , the spectral index is independent 
of the electron energy distribution and the theory predicts a value of 
2.5. Although the apparent effect of synchrotron self-absorption is 
evident in many sources and values of a = +1.0 are often observed at long 
wavelengths, no source has been observed with the a = +2.5 value predict- 
ed by theory. This might be explained by a gradual rather than an 
abrupt transition from the transparent to opaque condition, caused by a. 
range of opacities resulting from different parts of the source becoming 
opaque at different frequencies. Alternatively, O'Dell and Sartori 
(1970) have proposed "cyclotron turnover" as the possible low frequency 

cutoff mechanism. 

The spectrum shown in Figure 2a is referred to as a "complex" or 
"peculiar" spectrijm and cannot be explained by a single source of 
synchrotron radiation. Thus this type is believed to be a superposition 
of two or more curved or straight spectra, and is generally associated 
with compact radio sources. Because of their composite nature, such 
spectra often have relatively small values of spectral index over a 
portion of the frequency range and are thus sometimes referred to as 
"flat". A good correlation exists between composite radio spectra and 
violent optical and radio variability. The frequency at which self- 
absorption becomes significant is a function of the surface brightness 

2 

temperature (S / 9 ) , as is shown in equation (15) . Thus tor a given 
m 

flux, if the angular extent (6) of the active region is large, the 



23 



surface brightness temperature will be lower, resulting in a lower value 

of V . 

m 

The relatively good agreenent between theory and observations of 
the self-absorption cutoff frequency v^, the angular size of individual 
compact components as measured by VLBI, and the observed peak brightness 
temperature of 10^^ to 10^^^ K pose strong arguments that the radio 
emission from the very comapct sources is indeed ordinary, incoherent 
synchrotron emission (Kellermann 19 70) . 

Time Variations 



We finally come to the purpose of this research, which is to search 
for a relation between observed optical and radio variations. In general, 
time variations might be caused by 

a) changes in the rate of production or acceleration of relativ- 
istic particles; 

b) loss of energy due to synchrotron radiation, inverse Compton 
scattering, or adiabatic expansion; 

c) changes in magnetic field; 

d) (in the opaque region of the spectrum) changes in the angular 
size of the source as a result of expansion. 

In addition it should be noted that plasma ejection from a massive 
rotating body (spinar) could also be the cause of time variations. 
However, once the plasma has been ejected, any or all of (a) through (d) 
would apply. In fact it is most likely that all of (a) through (d) 
contribute to some degree among the different sources and at different 
periods of time within individual sources. 



24 



One unknown factor to keep in mind is that while we have strong 
evidence (from measured time of variations) that the optical, infrared, 
and high frequency radio flux come from very small regions, we do not 
know presently if these regions are one and the same or whether differ- 
ent parts of the spectrum arise from differnt regions. 

Expanding Source Model 

Based on short wavelength (2 to 10 cm) radio observations, the 
initial expanding source model assumed that radio emission from a vari- 
able extragalactic object is due to synchrotron radiation from a spher- 
ical cloud of relativistic electrons moving in a magnetic field while 
the cloud expands adiabatically . 

Shklovsky (1960) originally hypothesized the expanding source 
model, using it to predict decreases in radio flux from supernovae 
remnants. If we assume 

a) the electron energy distribution is a power law of the form 
given in equation (11) ; 

b) the magnetic field is fixed in the expanding cloud, so that 
magnetic flux is conserved, B^ = S (r /r^) ' ; 

c) each electron loses energy due to cloud expansion at a rate 
proportional to its energy, so that the form of the energy distri- 
bution is unchanged, that is E^ = E (r^ /r ) for each electron; 

d) no additional particles enter or leave the region, so that 



then for an optically thin source 



■2y 



^2 = ^1 7 



(15) 



1 I 



where r is the radius at time t^ and r^ is the expanded radius at 

time t„- 

However, examination of the radio spectra indicates that for a 
given frequency if we extrapolate back in time, at some point the density 
of relativistic electrons is such that the source is no longer completely 
transparent to its own radiation. At this point, from equation (15) the 
brightness temperature depends only on the value of the magnetic field, 
and the flux density is given by 



-1/2 2 5/2 
S(v,t) - B "-^^(t) 0^(t) v''^^ 



(17) 



If the expansion is constant in time and if the magnetic flux is 
conserved during expansion, then t. can be substituted for r^ in 
assiomption (b) , and equation (17) can be used to derive 



r,.-3 



S(t„) = S(t,) 



_^. 



(18) 



If the magnetic flux is constant, such that B(t^) = B(t^) , then 



S(t2) = S(t^) 



(19) 



In either case, the race of change of the flux density is independent of 
the electron energy distribution, because as long as the source is 



25 



optically thick, the observed radiation comes from only a fraction of 
the electrons. 

From expressions for the frequency v , at which the synchrotron 
self-absorption ceases, it can be shown that 



'ly + 3' 



S(v J 

m/ 

S(-:nl> 



Y + 4 



^ -.11 



ml 



4y + 6 



(20) 



Again it can be shotvn that the complete expression for flux density 
as a function of frequency v and time t is given by 



r 



S(v,t ) = S - 
2 ml V 



5/2 3/2 



ml/ 



1- 



exp 



Y+4 



-(2y+3)' 



M v^ 



m 



V 
V 

m 



-T 



m 



where S 



ml 



1-exp 
is the flux density corresponding to any frequency 



> (21) 



V ^ at time t, ; 
ml 1 



t„ is the time of observation at frequency v; 

T ' is the optical depth of any frequency v . 
m "1 

Ttius the model suggests that the varying components are sources of 
synchrotron radiation which initially are optically thick but become 
optically thin at progressively longer xi'avelengths as they expand 
(van der Laan 1966). The simple model predicts that outbursts will be 
seen earlier, and will have greater flux amplitude and a shorter outburst 
duration at higher frequencies. 

In principle, a measure of the radio spectrum at any time and its 
time rate of change miay be used to predict the future behavior of the 



27 



spectrum at all frequencies. In practice this is difficult because many 
variable source show multiple overlapping outbursts over short periods 
of time. In fact, long-term observations have shovm that repeated out- 
bursts of relativistic particles over time periods of a year or less are 
not uncommon in EGV's especially in the Lacertids. If one assumes that 
the expanding source model is valid, flares will be separated and better 
defined at higher frequencies due to shorter duration and less overlap. 
Extending this knowledge to lower frequencies can help identify the 
possible location in time of individual flares, from which the relative 
flare amplitude and duration may be estimated, within the constraints 
of the recorded flux level as a function of time. If this data can be 
obtained successfully, it allows one to study how a given event propa- 
gates in the frequency domain, and thus how it affects the spectral 
energy distribution. However, estimates of absolute amplitude and 
duration of a flare are almost impossible due to the difficulty in 
finding the quiescent radiation level. 

Expanding Source Model Difficulties and Alternatives 
While the model has been successful in quantitatively explaining 
centimeter variations from certain sources including 3C 120 (Dent 1968, 
Pauliny-Toth and Kellermann 1966, Seielstad 1974), discrepancies exist 
between 11.0 and 2.8 cm, and the theory appears to break down at short 
centimeter to millimeter wavelengths (Medd et al . 1968, Kellermann and 
Pauliny-Toth 1968, Lock et al. 1969, Kinman et al. 1974). The discre- 
pancies include incorrect form of the outbursts, lack of time delay 
and/or lack of amplitude change between events seen at different fre- 
auencies. The latter two discrepancies could be caused by the source 



28 



becoming optically thin, or by continuous injection of relativlstic 
electrons. Peterson and Dent (19 73) proposed a continuous injection 
version of the expanding source model with some limited success. Some 
of the additional modifications or combinations of parameters which 
might be tried include: variable expansion of the cloud; a mechanism 
to accelerate particles after an explosive event; possible escape of 
particles from the cloud; lack of conservation of magnetic flux; an 
expanding shell rather than a spherical cloud, introduced by van der Laan 
(1962) and Lequeux (1962); multiple interacting sources; relativlstic 
expansion (Ryle and Longair 1967, Rees and Simon 1968); non-isotropic 
radiation; coherent rather than incoherent radiation; changing electron 
energy distribution due to loss of energy by inverse Compton scattering, 
ordinary bremsstrahlung, and ionization. 

Thus there exists myriad possible combinations of parameters. Be- 
cause the simple model does have basic qualitative validity despite 
slgnigicant discrepancies, work is proceeding on revisions of the simple 
model. In particular, Peterson and Dent's limited success Xirith the 
obvious possibility of extended injection has motivated continuing 
investigations in that area. 

Peterson and King (1975) have attempted to extend the application 
of the continuous injection model into the optical wavelengths. Because 
of the gap in the observable spectrum between centimeter and optical 
wavelengths, it is not even known if a relationship exists between the 
activity observed at these two different frequencies. However, the 
limited observations at millimeter wavelengths indicate that the large 
and rapid variations predicted by the simple expanding rnxdel at these 
short wavelengths do not. occur. 



29 



Inverse Compton Scattering 

Inverse Compton scattering will take place in a region with a suffi- 
ciently large radiation density and a sufficiently strong magnetic 
field. Thus while this radiation mechanisin most likely functions in the 
types of sources under discussion, the main question that must be 
answered is how significant a role does this process play? The inverse 
Compton mechanism is highly inefficient and if a significant amount of 
the observed radiation is caused by the inverse Compton mechanism, the 
already awesome energy requirement increases much further. 

Inverse Compton scattering refers to the collision of a fast elec- 
tron with a low energy photon and the resulting production of a high 
energy recoil photon and a corresponding decrease in electron energy. 
The solution for the total spectrum of inverse Compton photons scattered 
per unit time and volume by a distribution of relativistic electrons 
passing through a photon gas is very complicated in the completely 
general case, and thus has not been attempted. However, simplifications 
result in limiting cases which have astrophysical applications. In the 

rest frame of the electron, if the energy of the photon before scattering 

2 
is much less than mc , the incident and scattered photons will have 

roughly the same energy and the scattering corresponds to the Thompson 
limit in which the Compton cross section is independent of the energy 
of the incoming photon. While in the laboratory frame, the character- 
istic energy of the scattered photon is large relative to the incident 
photon energy, it is still small compared with the electon energy and 
thus the electron loses a small fraction of its energy in any single 

inverse Compton scattering. However, in the limiting case where the 

2 
energy of the photon before scattering is much greater than mc , the 



30 



scattered photon carried ax^ay a large fraction of the electron energy, 
and thus the electron does not lose its energy continuously. 

Felten and Morrison (1966) present inverse Compton scattering in a 
manner that stresses its relationship with synchrotron radiation. Given 
a power law energy distribution of electrons as in equation (11), as 
long as the energy spectrum is not too steep, the distribution of recoil 
photon energies will be determined primarily by equation (11) , and will 
in fact be a power law distribution itself. 

The electron lifetime against synchrotron radiation loss is given 
by 

-312 -1/2 ,^^. 

t "- ^ V (22) 

s m 

where t is in years, B in gauss, and v in GHz; while the electron 
lifetime against energy loss to inverse Compton scattering (in the 
Thompson limit) is given by 

6 X 10 r9o>, 

t % : (23) 



where t is in years and p is the energy density of the surrounding 
c 

3 
radiation field (photon distribution) in eV/cm . To give an example of 

the significance of the radiation energy density on inverse Compton 

losses, consider a 5 GeV electron (y ^^ 10 ) trapped in the galaxy where 

p '^^ 10 eV/cm compared to one trapped near the solar surface where 

12 3 
p "^ 2 X 10 eV/cm . In the galaxy, the electron will have a lifetime 

TO 3 

t -^^ 10"^ years, whereas near the solar surface, t '^^ 10 sec. 



31 



The total instantaneous power scattered by an electron is given by 

4 

Q n 

where a is the Thompson cross section (a = T^^o ); whereas the 
instantaneous synchrotron power radiated by an electron is given by 

7 2 2 2 
P (y , H) = ^ r ^ cy B^ (25) 

s r 3 o r 

where r^ is the classical - electron radius and c is the velocity of 
light. Thus the ratio of the two powers for a single electron is given 

2 2 "> 

P (y ,B) r cy (H sinO ) 
s r o r e 



P (y >P) /Tc /ON 2 2 
c r (16iT/3)r cy p 

or 



3 B /8tt ] . 2. ,.,. 

sm (28) 

2 ^ p I e 



Then assuming that the electron velocity is randomly oriented V7ith 

respect to the magnetic field, the time or ensemble average gives 

2 ■^ 
< sin 6 > = ^ ; and thus 
e J 



P „2 
P 



s a /8iT ^27) 



c 

where (B /Sir) is the energy density of the magnetic field. Thus the 
ratio of losses from synchrotron radiation and from inverse Compton 
scattering is equal to the ratio of the energy densities. (Note that in 
some notation H is substituted for B, but as long as consideration is 
limited to vacuum, B = H.) The assumption of equipartition of energy 



32 



between the energy density of the magnetic field and the energy density 
of the radiation field requires the least total energy from a source. 
If the energy of the radiation field exceeds twice the energy density of 
the magnetic field, catastrophic inverse Compton losses result, 

Kellermann and Pauliny-Toth (1969) have expressed these conditions 
in terms of the maximum brightness temperature (T ) observed in compact 
sources. According to their development, for a homogeneous and isotropic 
source, the intensity of the radiation from inverse Compton scattering 
relative to the intensity of radiation from synchrotron em.ission (L^/L^) 
is given by 



c s 



c „ 1 



m 



2 i 12 
^ ' 10 



1 + 



m 



10 



12 



m 



(28) 



11 



where v is the cutoff frequency in ^ffiz due to synchrotron self-absorp- 
m 

tion. Assuming a roughly typical value of v '>^ 100 GHz, if T^ < 10 K, 

L /L « 1 and inverse Compton scattering is insignificant. But if 
c s 

T > 10 K, the bracketed term., which represents the effect of secona 
m 

order scattering, becomes important and L /L 'v (T /lO ) . Thus it 
° c s m 

is argued that the catastrophic energy losses due to inverse Compton 
scattering "cool" the source, causing a decrease of T to between 10 

to 10 K, where losses to both processes are roughly the same. As an 

11 
example, assume that v '\> 1 GHz. Then for T -v- 10 K, the half-life of 

m m 

/ 12 

an electron is '^^ 10 years, whereas if T '^ 10 K, the half -life drops 

to about a day. 

Felten and Morrison developed still another expression relating the 
radiation intensities, which may prove useful. 



33 



^ v^s s „ B /8tt 

r\j — — — '\j 



(I ) K 
V c c 



2 X 10 T ' 



( 3-y ) 
2 



(29) 



where K and K represent the constants and parameters entering the 
s c 

respective coefficients. They then use that expression neglecting 
inverse Compton scattering from the 3 K background radiation to compute 
the expected spectra from synchrotron and inverse Compton radiation for 
the galactic halo with an imposed high frequency cutoff, as shown in 
Figure 4. Conditions in the galactic halo are far different from con- 
ditions in compact variable sources; the point is that if both syn- 
chrotron and inverse Compton components exist and can be resolved in 
an observed spectral energy distribution, equation (29) will provide 
a useful estimate of physical conditions in the source. 

Finally, a relation between the characteristic synchrotron fre- 
quency (v ) emitted by an electron at a given energy, and the charac- 
teristic energy (e ) of the Compton scattered photon is given by 

<£,> ^ 0.9 X 10^ ^ V (30) 

1 ^1 *^ 

where e is in eV, B, in y-gauss, and v^ in l>fflz. From this it can be 
seen that for a given brightness temperature T, the characteristic 
Compton scattering energy, and therefore frequency, decreases for in- 
creasing magnetic field strength. (It should be noted that in my 

notation, Y , Y, 9 , and v correspond to Felten and Morrison's y , m, 
're c 

^, and V .) 

In summary, it should be em.phasized that values of the magnetic 
fields and electron half-lives against inverse Compton scattering can 
be estimated using equations (15) and (28), without assuming a distance 



34 




2 2 

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35 



to the source or equipartition of energy. Possibly large uncertainties 

do exist in the determination of the angular size (6) and cutoff fre- 

Quencies (v ) , especially in sources possessing complex brightness 
m 

distributions which are characteristic of EGV's. 

If the distance to the source is knoxro, the energy content of the 

relativistic electrons, E , and the magnetic field, E^, can be uniquely 

determined (Kellermann and Pauliny-Toth 1969). However, for typical 

spectral indices (y '^^ 2.5) the ratio E^/E^ depends on the 'V'20th power 

of the cutoff frequency, v , and the angular extent 8; thus departures 

m 

from energy equipartition are difficult to detect. 

The major controversy centered around synchrotron radiation versus 
inverse Compton scattering is based on the lifetimes of electrons 
against energy loss. If one assumes, based on an "average" outburst 
duration, a typical size of ^10"''^ cm (one light month) for an active 
region, this implies lifetimes of the relativistic electrons of approx- 
imately that same length. Thus some argue that it is unlikely that any 
significant portion of the emitted radiation could be due to inverse 
Compton scattering, because that would imply electron lifetimes as 
short as one day. From this point, Hoyle, Burbidge, and Sargent (1966) 
calculated the ratio of magnetic to radiation density assuming synchro- 
tron radiation was the dominant process and the source 3C 273 was at a 
cosmological distance. The resulting ratio of energy densities indi- 
cated catastrophic inverse Compton losses, from which they concluded 
that the source was not at a cosmological distance. However, Woltjer 
(1966) countered by assuming a non-isotropic radiation field, explained 
away the energy density problem and put 3C 273 back at cosmological 
distances. This presents a specific example of the controversial 



36 



nature of this research. 

The considerations listed here have prompted some to develop 
radiation models which include both synchrotron and inverse Compton 
radiation (Takarada 1968, Cavaliere et al. 1970, Rees 1971, Blanford 
and Rees 1972). 

Optical Spectra 
To study the absolute energy distributions of EGV's at optical 
wavelengths, data recorded as stellar magnitudes are converted to an 
energy scale using the absolute energy distribution of aLyra as a 
reference. This source was calibrated by Oke and Shild (1970), who 
formulated a conversion expression 



m 



= -2.5 log F - C (31) 



where m is the magnitude, F is the corresponding energy flux in units 
of 10^^ Janskys (1 Jansky = 10~^^ Watts/m /Hz) and C is a constant. 
For all conversions made in this study, C = 56.04. 

Extragalactic variables that exhibit large amplitude optical vari- 
ations are usually those that have significant optical polarization, 
steep power law optical spectra, and that tend to be associated with 
compact radio sources having flat radio spectra at gigahertz frequencies 
(Kinman 1975). The non-thermal continuum of the Seyfert galaxy 3C 120 
is relatively flat in the UV, increases towards the red in the visual 
range and turns up sharply in the IR (Shields et al . 1972), as shown 
in Figure 5. This appears roughly similar to the energy distribution 
of the QSO 3C 273. 



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39 



The optical and near infrared spectral distribution of BL Lac and 
OJ 287 are presented in Figures 6, 7, and 8. The Lacertids in general 
exhibit approxiiaate power law spectra which grow steeper (more nega- 
tive) between the near infrared and the optical as can be seen from the 
values in Table 3, from Rieke and Kinman (1974) and Oke and Gunn (1974), 
Tne somewhat flatter infrared index may be the result of positive 
curvature in the non-thermal spectrum and inclusion of some stellar 
radiation at 2.2y. (Note that for BL Lac, the values for the infrared 
and the optical spectral indices were derived from observations that 
were separated in time.) 

TABLE 3 
LACERTID OPTICAL AND NEAR-IR SPECTRAL INDICES 



SOURCE 


IR 
(10. 5y - 0.44y) 


OPTICAL 
(0.55y - 0.36u) 


0735 + 17 


-1.20 + 0.15 


-1.9 


OJ 287 


-0.86 




ON 231 


-1.13 + 0.12 


-2.0 


EL Lac 


-1.15 + 0.2 
(10. 5y - 2.2y) 


-1.55 

(<iy) 



Caution must be exercised when comparing optical spectral indices 
of such violent variables because the variations do affect the spectra, 
as will be discussed. In addition, while BL Lac has no emission lines, 
if it is at the nucleus of an ordinary giant elliptical galaxy, as is 
indicated by the work of Oke and Gunn (1974) , then it may have a sig- 
nificant stellar component at optical wavelengths, which is presumed to 
disappear at lOy (Rieke and Kinman 1974). Its optical spectrum at 



40 






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44 



wavelengths <lu shows significant variations and can be represented by 
a power law of index a = -2.85 to -3.17, as shown in Figure 9; thus it 
exhibits one of the steepest spectra observed. By contrast, the slope 
of the optical spectrum of OJ 287 does not show strong time variations; 
it may steepen slightly with increasing frequency. The measurements 
used in Figure 8 were made at different time than those of Rieke and 
Kinman, and they can be fitted quite well by a straight line of slope 
a = -1.248 (Visvanathan 1973b), 

At the time of observation (Oke _et_ al. 1970) , the optical continua 
of twenty-eight quasars between . 3y and 2.2y could generally be approx- 
imated by power law spectra having indices of a = -0.2 to -1.6, with 
the entire range being populated, as seen in Figures 10, 11, and 12. 
However, the presence of broad emission lines combined with limited 
spectral resolution makes it difficult to determine if the continuum 
is power law or curved from this data. Observations from '^ 0.9 to 0.4u 
by Visvanathan (1973a) of three of the most active quasars, 3C 345, 
3C 446, and 3C 454.3, indicate that these optical continua can be rep- 
resented by a power law in both active and quiet phases, as illustrated 
in Figure 13. Observations such as those in Figure 13 have yet to in- 
dicate any relation between optical activity and quasar color in any 
individual source or among the sources as a group. Sometimes the QSO 
grows redder (mora negative slope) during activity, while at other times 
it grows bluer. This lack of relation between brightness and color may 
be an indication that the continuum source region consists of many 
centers of activity, but it also raises the question of whether there 
might be material in the general region of the quasars but not 



»'-=?l*"- 



45 







BL 


_AC 






— — 1 1 1— 


1 1 


, .^ , 


1 


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. 




\ 

• 

\ 

\ 




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\ 




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\ 




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\ 






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OCT 20, 1968 


^ 


JULY 16, 1969 


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\ ; 


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- 




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- 


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\ 


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• 


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- AUG 19, 1969 


• DEC 5, 1969 


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a-- 2 93 ± 0.04 


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1 1 


'. . \ 1 1 1 


; ^ 



14.5 



14.7 



14.9 14.5 

log ly 



14.7 



14.9 



Figure 9. BL Lac: continuum measurements of the optical spectrum, on 
different days, indicating change of power law index. Straight lines 
are least squares fits for alj. the continuum points. Reproduced from 
Visvanathan (197 3a) with permiission of the author and The Astrophy sical 
Journal, which is published by the University of Chicago Press. 



53 



immediately associated with them, whose character or nature changes 

with time. 

Kinman (1975) argues that in the case of the Lacertids, variations 
of the optical spectral index do not merely consist of changes in the 
slope of a power law relation, but also consist of variable curvature 
in the energy distribution. However, observations by Rieke and Kinman 
(1974) and by Smith _et al. (1975) indicate that the UBV color of OJ 287 
remained constant during a long-term decline of three magnitudes in its 
mean brightness, with short-term changes in the color which have not 
yet shown any relationship to the short-term changes in brightness. 
In addition, the observations of Smith et_ al. contain some evidence for 
a slower rate of decline in the infrared, in contradiction to the 
10.5-y observations of Rieke and Kinman, However, Kinman (1975) states 
that the spectral index becomes flatter tox^ards the infrared. 

All classes of extragalactic variables, especially the Lacertids, 
exhibit significant linear optical polarization (Kinman et al. 1974); 
in addition, 3C 279, 3C 345, 3C 446, 3C 454.3 and BL Lac have shown 
changes in the polarization position angle during bursts as compared 
with the position angles before and after activity. This has been 
interpreted as an indication that changes in the magnetic field config- 
uration of the region emitting the continuum is a characteristic 
feature of the burst phase of these sources (Visvanathan 1973a) . 
Moreover, observations of both radio and optical polarization in 3C 345 
and 3C 454.3, for 2 and 1 years respectively, indicated agreement in 
the measured position angles in 3C 345, but disagreement in 3C 454.3. 
In the case of 3C 345, this can be interpreted to mean the optical and 
radio emission came from the same region. This is vital information if 



54 



one is trying to correlate activity at different wavelengths from a 
multiple-component source. In the case of 3C 454.3, one interpretation 
is that the radio and optical continua originate from different volumes 
of space, but this may come about in two different ways. If a correla- 
tion exists between optical and radio observations, a single source may 
emit the optical radiation observed at time t , then undergo an expan- 
sion and a change in magnetic field configuration before emitting the 
radio radiation observed at time t, + At. On the other hand, the optical 
and radio emission may arise from two different, spatially separated 
sources. 

The non-thermal character of the optical continuum emission from 
extragalactic variables appears generally accepted. The observations of 
apparent power law spectra at optical xjavelengths , rapid variability/, 
and linear polarization which appears to be independent of wavelength, 
leads to a conclusion by many that the optical continuum has a synchro- 
tron origin. Inverse Compton scattering has also been suggested, but 
the lack of detection of an X-ray flux from almost all these sources 
sets an upper limit to the X-ray flu>: V7hich is apparently incompatible 
with the X-ray flux expected form inverse Compton scattering. Further- 



more, 3500 to 8000 A observations of 3C 345, 3C 446, 3C 454.3, and 
BL Lac between 1968 and 1969 again indicated that both the degree of 
polarization and the position angle were independent of wavelength. 
This strongly suggests that the same mechanism is responsible for the 
continuum radiation in these sources from ultraviolet to infrared 
wavelengths. 



55 



Galactic Infrared Radiation 

Infrared astronomy is still in an early stage of development be- 
cause the atmosphere restricts ground-based observations to roughly the 
1 to 20 y range. Observations at longer wavelengths are made from 
balloons, aircraft, rockets, and high altitude observatories. As previ- 
ously noted, extragalactic variables in general show as infrared excess 
and, as shown in Figure 1, some emit the majority of their luminosity in 
the infrared. Attempts to explain this radiation must be based on what 
we have learned about sources of infrared radiation in our own and in 
other galaxies. Figure 14, while dated (Low and Aumarni 1970), gives a 
summation of the infrared observations of the H II regions Orion A and 
M 17, the galaxy M82, and the galactic nucleus Sagitarius A. More 
recent data from Telesco et al . (1976) has been included for the Seyfert 
galaxy NGC 1068. Again dashed lines connect known measurements at the 
time of publication. 

A significant amount of the infrared radiation in our galaxy is 
thermal radiation from dust particles or grains, which both scatter and 

o 

absorb incident radiation. Absorption of starlight from 3000 to 10,000 A 
increases with increasing frequency, causing an extinction or "reddening" 
as illustrated in Figure 15 (Greenberg 1968). The absorbed radiation 
heats the grains, thus redistributing higher frequency radiation into 
the infrared. 

An infrared excess refers to an amxOunt of radiation within a given 
infrared radiation interval which is in excess of what would normally be 
expected from the type of source observed. Such excess infrared radi- 
ation in our galaxy arises from H II regions, some hot Be and Of stars, 



Figure 14. Spectral energy distributions of galactic and extragalactic 
sources. Dashed lines indicate a lack of data for that wavelength 
interval. Upper limits are indicated for M82 at 70 u and Sgr IRA at 
1000 y. Reproduced from Low and Aumann (1970) with permission of the 
authors and The Astrophysical Journal, which is published by the 
University of Chicago Press. More recent data obtained from Telesco 
et al . (1975) and Rieke and Low (1975) were used to plot the curve for 
NC-C 1068. 



3 J 



3cm 



3mm 



300/1 



M 



CVJ 



I 

CD 



LU 

X 



o 
o 



.^\ 



30/x 



Sqr IRA 



3fM 




11 



12 13 

LOG FREQUENCY (Hz) 



M17 

RA 
AND !RB 



Sgr IRA 



NG 1068 



14 



58 



X(^ 



h- 
X 







Figure l!). Schematic diagram illustrating extinction or "reddening" as 
a function of frequency and xvavelengtb. . 



59 



protostars which are believed to exist in dense gas and dust regions, 
circumstellar grains surrounding stars, and the galactic nucleus, which 
is a highly luminous infrared source whatever its nature is. 

Observations indicate that a significant fraction of both inter- 
stellar and circumstellar grains are silicate particles similar to 
material returned from the moon, thus indicating a possible relationship 
between the material found in galactic interstellar space and that from 
which the bodies of the solar system may have formed. In addition, 
infrared obser>/ations of early hot stars can be interpreted as arising 
from free-free emission of ionized hydrogen; observations of planetary 
nebulae may indicate that grains can condense in high velocity fields 
within destructive ultraviolet radiation fields, that is in almost any 
environment where the grain temperature is maintained below its evapo- 
ration temperature; and limited observations of novae indicate that 
material ejected during stellar mass loss can condense into dust 
particles (Stein 1975, and Neugebauer et al. 1971). Furthermore, infra- 
red observations of H II regions have provided evidence that grains can 
exist in ionized regions and that the emission can arise from grains at 
different temperatures (Wynn-Williams and Becklin 1974). 

The galactic nucleus is complex but can be represented by three 
main components defined by their spatial and wavelength distributions 

o 

as follows: an extended source measured over a 1 region and observed 

o o 

between 1 and 5 y; a 2 x 4 source which has fine structure and is 
found at 100 u; a 15" source coincident with the non-thermal radio source 

Sgr A. The galactic center up to 100 y has an estimated infrared 

9 
luminosity of 10 L , x^hich is much less than the infrared emission irom 

extragalactic variables. Most of the 1 to 5 p emission is believed to 



60 



be stellar radiation, altered by about 30 magnitudes of visual absorp- 
tion, from a high spatial density of stars. Observations of the nucleus 
of M31 show similar characteristics. Tae origin of the 100-vi flux is 
unkno^^ra, although a significant portion again may be thermal re-radia- 
tion of starlight. Of most interest here is the 15" (0.7 pc) source 
which radiates between 3 and 20 y with an energy distribution that can 
be approximated by a power law of slope a - -2. Thus it resembles the 
spectra of the nuclei of several extragalactic variables and leads to 
obvious speculation about similar physical processes involved. The 

radiation from this source could be due to a reasonably sized dust cloud 

3 
of mass > 3 X 10 M surrounding a concentration of stars or some other 

source of energy. It might also be non-thermal but this is unclear for 

a number of reasons. While the 15" source is coincident with Sgr A, the 

non- thermal radio emission from the latter comes from an area five times 

the diameter of the infrared source. In addition, the flux density at 

20 y is ten times greater than the radio emission at 2 cm, which is in 

disagreement with the characteristic spectral energy distribution of a 

non-thermal radio source (Neugebauer et aJ . 1971). However, there may 

be two different energy sources, or one might trj^ to construct a model 

2 

for opacity at infrared wavelengths. In addition, approxim.ately 10 

12 
identical sources of B . 'v. 30 gauss and radius 10 cm could emit the 

mm 

observed flux. The existence of multiple small sources may not be 
unreasonable considering the strong evidence of almost continuous 
activity in som.e galactic nuclei. 



61 



Extragalactic Infrared Hadiation 
Estimates of the infrared luminosities from extragalactic variables 
are tentative to unreliable because of the lack of observations between 

50 to 300 y. However, extragalactic variables are characterized by 

10 11 
infrared Iximinosities of 10 to 10 L_ (Neugebauer et al. 1971 and 



Telesco _et_ al. 1976) and total Seyfert emission in the infrared may be 

44 47 
as high as 10' to 10 ergs/sec (Rees _et al. 1969). In addition, a 

sample of infrared spectra from Seyfert nuclei indicates that they can 
be characterized by a power law of index a = -1.5 to -2.0. In this 
wavelength range, NGC 1068 may have a more negative power law index, and 
a correspondingly steeper spectrum. In particular, between 28 and 320 y, 
NGC 1068 has a luminosity equal to 3,7 x 10 L . It should be noted 
that while some members of the specific class of compact galaxies (as 
distinct from the general class of EGV) have infrared excesses similar 
to Seyfert galaxies, others do not show any conspicious infrared excess. 
A sample of 30 QSO's show spectra that can generally be characterized by 
indices of a = -0.2 to -1.6 from 0.32 to 2.2 p., although some clearly 
show curvature. Stein (1975) observes that the infrared spectra of 
OJ 287 and BL Lac are generally flatter (a ^ -1) than the infrared 
spectrum of sources such as NGC 1068 (a "^ -2) , and he then speculates 
that some sources may emit both thermal and non-thermal infrared radia- 
tion. Not all Lacertids have been detected or even observed in the 
near- infrared. 

Variations of the 2.2-y infrared flux on a time scale comparable to 
the measured optical variations have been observed for 3C 279, 3C 345, 
3C 446, and 3C 454.3, which are among those sources having the steepest 



62 



rise in their energy distributions at infrared wavelengths and which 
exhibit short duration large amplitude optical variations (Oke _et_ al . 
1970) . In addition, it is argued on the basis of the infrared and visual 
spectral distributions in Figure 12, that to within the limitations of 
simultaneous measurement, the infrared and visual variations follow one 
another. If this is true, it would indicate that for these sources the 
same mechanism is probably responsible for the production of radiation 
from the infrared to the ultraviolet. 

Rieke (1972) and Kinman e_t al. (1974) have provided evidence for 
both long-term (years) and short-term (months) variations in OJ 287 
between 2.2 and 10 y. Rieke contends that these short-term infrared 
variations correspond in extent and time with B-magnitude and millimeter 
observations made at the same time. Kinman et_ al . established a very 
strong correspondence in long-term activity over the same wavelength 
range. Rieke also observed possible evidence for infrared variations of 
BL Lac in the 2 to 20-y range but the data are sketchy. Significant 
short-term variability of BL Lac at 2.2 y is believed to exist 
(Neugebauer et_ al. 1971) . 

No satisfactory explanation of the infrared emission from extra- 
galactic sources has yet been found. Thus far, observations of some 
sources provide evidence that both thermal and non-thermal radiation is 
present. Neugebauer e_t al^. have observed that knowledge of the energy 
distribution between 20 and 500 y is critical to any investigation of the 
radiation mechanism. VThile any discussion of detailed models is 
probably premature until that data is available, I will briefly review 
the speculations. 

Of course there are two possible radiation mechanisms; thermal 



63 



re-radiation by dust grains and non-thermal radiation by incoherent 
synchrotron or inverse Compton scattering. It is generally agreed that 
very short-term (less than a few weeks) variability of the infrared 
radiation or significant as well as variable infrared polarization would 
imply a non- thermal source. However, to date there has not been conclu- 
sive evidence of either of these characteristics. 

The proponents of thermal radiation argue that small grains may 
condense during the expansion phase following a violent outburst and that 
the observed energy distribution is obtained by the superposition of 
several different blackbody curves corresponding to shells of dust at 
different distances from the source. A.s noted earlier, there is evidence 
for the existence of dust in or near Seyfert nuclei and quasars (Burbudge 
and Stein 1970). While the amount of dust required for such emission 
appears physically reasonable, its required size does place lower limits 
of a few weeks to a month on the allowed time scale of variations at 
wavelengths 5 10 y. Variations on a shorter time scale have not yet been 
conclusively established. The discovery of slight polarization could be 
explained by emission from magnetically aligned grains. 

The proponents of a non-thermal mechanism argue that while there is 
evidence of dust near active sources, it is too far removed and of too 
little quantity to cause the observed infrared flux. The main difficult- 
ies in the case for non-thermal emission are the need for a sharp cutoff 
at low frequencies and the condition that inverse Compton scattering 
losses not exceed synchrotron losses. Burbidge and Stein (1970) conclude 
that the energetics of a synchrotron model are physicallj' reasonable 
because total required energies are less than those required to explain 
the compact radio sources or to explain non-thermal optical radiation. 



64 



but require magnetic fields of "-- 1 to 100 gauss. They also point out 
that in some cases, the data support the hypothesis of nuclei consisting 
of a large number of separate components. Cavaliere et^ _al • (1970) 
propose a model which emits both synchrotron and inverse Compton 
radiation. 

During the writing of this summary of research efforts, I was struck 
by the analogy to an earlier attempt to explain a troublesome spectrum, 
that of the blackbody. If we can explain the spectrum, most likely we 
can explain the source. However, we must first have the whole spectrum! 



CHAPTER III 
ANALYSIS OF THE LONG-TERM OPTICAL AND RADIO RECORDS 



The Research Problem 

Up to ten years of observations of the sometimes violent optical 
and radio variations of extragalactic variables have compelled many to 
ask the potentially important question, Are the optical and radio varia- 
tions for a given source correlated? The gap in the observable spectrum 
between millimeter radio radiation and optical radiation makes it 
impossible to follow an event through the intervening spectral range and 
necessitates attempts to correlate radio and optical variability before 
one can test a model against data taken at these separated wavelengths. 
If a relationship exists, then what are its characteristics and its 
implications with respect to the emission mechanism.s just summarized? 
At the same time, if no relationship exists, what are the implications? 
As I have indicated by the summaries in Chapter II, the answers to these 
questions are very important for defining the radiation mechanisms and 
modeling the source of radiation. In addition, such information is 
necessary for the planning of cooperative multi-wavelength observing 
programs. For the first time, collections of observations are reaching 
the point where meaningful investigations of such correlations on a time 
scale of many years can be made. 

A visual inspection of the optical, millimeter, and centimeter data 
for a few extragalactic variables reveals variations that are comparable 



65 



66 



in time and, in some cases, amplitude. This is both promising and 
hazardous, because one must be careful to avoid chance correlations 
between random events that are not really related. Most searches for 
correlations have examined the short-term variations of 3C 120 (Usher 
1972), OJ 287 and BL Lac (Kinman and Conklin 1971; Andrew e^ al . 1971; 
Epstein et_ al. 1972; Andrew et al. 1974; Kinman et al. 1974; Miller et al. 
1974) and the long-term activity of 3L Lac (Hackney e_t al. 1972) , and 
OJ 287 (Lyutyi 1973). 

The Radio and Optical Data Records 
The Rosemary Hill Observatory of the University of Florida, the 
Algonquin Radio Observatory, the University of Massachusetts, the Royal 
Greenwich Observatory, and the Yale University Observatory have monitored 
extragalactic variables at radio or optical wavelengths for a number of 
years. The present study examines these long-term records in an attempt 
to discover correlated activity for sources common to the monitoring 
programs. It makes use of Rosemary Hill blue or photographic magnitudes 
(McGimsey et al. 1975; Scott et_ al . 1976), Algonquin 2.8-cm (10.7 GHz) 
data (Medd et al. 1972; MacLeod e^ al . 1975), University of Massachusetts 
1.9-cm (15.5 GHz) data (Dent e_t al. 1974; Dent 1976), Royal Greenwich 
Observatory optical m.agnitudes (Tritton and Brett 1970; Cannon et al . 
1971; Tritton and Selmes 1971; Selmes et_ al . 1975), and Yale Observatory 
photographic magnitudes (Lu 1972). In addition, blue magnitudes from 
the Goethe Link Observatory were used for 3C 273 (Burkhead and Parvey 
1968; Burkhead 1969; Burkhead and Lee 1970; Burkhead and Stein 1971; 
Burkhead and Rettig 1972; Burkhead and Hill 1975). 



67 



For the first time, the extensive records from the above observa- 
tories have been integrated and presented together in figures accompany- 
ing the textual presentation for each source. Thus, these figures 
represent a relatively complete documentation of the available observed 
long-term radio and optical variations (or lack thereof) . The raw data 
have been plotted with one-rms error bars. In several cases, data from 
different observatories were combined to obtain a longer data record. 
I acknowledge that this is a potentially hazardous procedure for any 
quantitative analysis for three reasons. First, different optical 
observatories may use different comparison sequences: and while Rosemary 
Hill B magnitudes are filtered (GG-13) exposures taken with a reflector. 
Royal Greenwich B-magnitude plates are unfiltered exposures taken with a 
refractor. Second, there is often a time delay and an amplitude differ- 
ence between the Dent 1.9-cm data and the Algonquin 2.8-cm data, as one 
might expect from the expanding source model. Third, the calibration of 
the absolute flux density scale m.ay differ between two radio observatories, 

Hovrever, for visual presentation of long-term trends in the data, 
the effects of the second factor are generally negligible. To m.inimize 
the effects of all three factors, in most cases where different sets of 
data were combined to form a single radio or light curve there was 
sufficient overlap between the sets to establish that the variability 
information was essentially identical for both sets (to within less than 
one rms error) and to measure the zero-point offset between the two sets 
if such an offset existed. The empirically determined offset was then 
applied to the shorter of the two sets to create a consistent long-term 
record. 



68 



Cross-Correlation Analysis 

The long-term optical and radio data records have been examined 
visually with great care to search for evidence of correlation. This 
was accomplished by plotting the two data records on different sheets, 
literally laying one curve on top of the other, and sliding one with 
respect to the other in search of coincidences between the two records. 
Then, as a first attempt to search analytically for correlations, the 
optical magnitudes and radio fluxes were linearly cross-correlated. 
Unf orttmately, long-term astronomical measurements are almost invariably 
spaced unevenly in time because of the monthly and annual cycles imposed 
by the moon and the sun, with additional interruptions being created by 
equipment failure, weather, and scheduling. 

Because of the mathematical difficulties associated with treating 
unevenly spaced time series, it is common practice to fit a curve to the 
data, thus creating a continuous function which can be used directly or 
sampled evenly for analytical study. However, this requires the choice 
of a fitting function, thus introducing a certain bias into the data. 
This is particularly important in studies of rapid, large- am.plitude, 
random variables where two or more outbursts may be superimposed, the 
character of each individual outburst is not known, and the data lost 
in observation gaps are unpredictable. 

For these reasons, in an attempt to avoid biasing the raw data, I 
chose to synthesize evenly spaced time series by stepping through the 
radio and optical data records for a given source hj an increment of 
time At^ , averaging all data falling within that increment, and either 
linearly interpolating or leaving a "hole" for those time increments in 



69 



which no data were taken. Next the total record of radio data was 
shifted backwards in time relative to the optical by an amount At^^. 
The radio record was then moved forward in time by steps of At , 
(At„ 5 At ) while a normalized linear cross-correlation coefficient, R, 
was calculated for all overlapping data for each increment of At • For 
any value of the time shift At (At = nAt - At„), coincidences between 
radio data and optical holes, or vice versa, were not used in the calcu- 
lation of the correlation coefficient. This procedure was followed 
until the radio data had undergone a total time shift of 2At„. 

For this study, the following formula , was used to calculate the 
normalized cross-correlation coefficient, R, for each value of At, 



Z (x y ) -y (Zx ) (Zy ) 

R(At) = rj^ (32) 

rv 2 1 .- n2/^ rv 2 1 .2.1/2 
[Zx. - - (Lx.) ] [Zy. - - (Z, .) J 



where x and y are functions of time and N is the number of coincidences 
between radio and optical data increments. This can be shown to be 
exactly equivalent to the more classical formula for R (Harnett 1970) , 

Z (x - x) (y - y) 

R = ^^ Yn '^^^ 

[Z(x^ - x)^ Z(y^ - y)^] 
by the use of the following identity: 

Z(x_. - x) = (x. - x) + (x, - x) + ... (x,,^ - x) 

= (Zx.) - Nx (34) 



70 



The technique just outlined has a number of characteristics that 
should be noted. 

a) The original optical and radio data records resulted from 
irregularly sampling two continuous functions of time. The correla- 
tion coefficients are calculated for synthesized, evenly spaced 
time series which are assumed to represent the long-term functions 
of time. 

b) Observational errors are not considered in the calculation of 
the time averages or the correlation coefficients. 

c) The calculated correlation coefficients are partly a function 
of the choice of At, , which is itself dependent on the time resolu- 
tion of the data and the time scale of the observed activity. 

d) Attempts to correlate too small a data sample result in spurious 
coefficients which, when plotted as a function of At, form a scatter 
diagram. l-Tnen this occurs for the overlap of the beginning of one 
data set with the end of the other set it is referred to as an 
"edge effect". 

e) Wlien each of the two records has only a singly significant peak 
or "bump", the records will be strongly correlated for some value 
of At even though there may be no physical relation between the two 
events. Great caution must be exercised in the consideration of 
such "one-event" correlations. 

f) Because I am cross-correlating unevenly space time series and 
examining a population of cross-correlation coefficients, the 
classical test of significance is at best questionable and at worst 
simply not applicable. It is included in Table 4 only for lack of 
a better statistical method, and it should be used in conjunction 



71 



with a careful and skeptical examination of the data records 
themselves , 

g) The precision of At is limited by the choice of At . 
h) The statistical technique used, equation (32), calculates a 
normalized linear cross-correlation coefficient between two 
functions which are represented by time series; however, radio flux 
is linearly proportional to the emitted energy while an optical 
magnitude is proportional to the log of the emitted energy. Thus 
strictly speaking this technique measures the relation between 
emitted radio energy and the log of the emitted optical energy as 
a function of time shift At. This was done because of the 
following: 

1) Most investigations involving optical data are both con- 
ducted and published using a magnitude scale to represent the 
data. 

2) Presentation of the optical and radio data on the same 
graph in a form that is easy to examine necessitated the use 
of both radio flux and optical magnitudes. 

When a potentially significant cross-correlation was found, a 
regression plot of radio flux vs optical magnitude was made to illustrate 
and investigate the functional relationship between the two sets of 
data. The regression plots were obtained by shifting the synthesized 
time series by the value of At that gave the maximum correlation 
coefficient. 

It is difficult to justify the use of linear interpolation to fill 
observational gaps in the data records because we have no knowledge of 
the emission intensity during that gap. Thus the interpolated data 



72 



records must be used cautiously, and the validity of results from the 
interpolated data records must be examined for each source independently. 
In general, for any given source the hole technique and the interpola- 
tion technique yielded similar results. Thus, because the hole 
technique more nearly approximates the original record, the results of 
this technique alone are summarized in Table 4 (Chapter IV) . 

Choice of Correlation Parameters 

As noted previously, the value of the correlation coefficient and 
its distribution as a function of At do depend on At , which is deter- 
mined by the character of both the optical and radio data records. 
Thus a trial and error method of using different values for At^ and At„ 
was employed to find the "best" values. 

Obviously it makes no sense to use a At^ smaller than At because 
this oversamples the resolution of the data introduced by At . However, 
ome might use a At larger than At to accentuate long-term effects when 
working with high time resolution data sets. In general At„ should 
equal At . The choice of At„ of course depends on the relative coverage 

JL ^ 

of the optical and radio data records. If correlation coefficients are 
calculated when the extent of the overlap between the optical and radio 
data is less than 10%, and in some cases 20%, of either the entire 
optical record or the entire radio record, then edge effects or spurious 
"one-event" correlations arise. Therefore At^ was usually chosen to 
calculate the correlation coefficient for all overlaps involving m.ore 
than 10 to 20% of the whole of both data records. 

The choice of the "best" values for At and At. x<ras of course a 
subjective judgement based roughly on the following criteria. 



73 



For the cross-correlation calculation, a) I'Jhat was the smallest value of 
At for which R vs At remained a smoothly varying function? b) Seconda- 
rily, what was the value of At that yielded the maximum correlation 
coefficient? For the regression plots, a value of At^ was chosen which 
yielded a "sufficient" number of points to suggest a possible relationship, 
In the following presentation of the results, graphical summaries 



o 



f R vs At for more than one value of At are sometimes presented to 



1 



illustrate the effects of the choice of At^, 



CHAPTER IV 
RESULTS OF THE CORRELATION ANALYSIS 



The results of the analytical study are summarized in Table 4, where 
column one gives the source name; column two the maximum cross-correla- 
tion coefficient, R, corresponding to the time shift At listed in column 
three; column four lists the number N of increments in the synthesized 
time series that contained data and were used to calculate the maximum 
cross-correlation coefficient; and column five gives the confidence level 
for the maximum value of R calculated from the two-tailed Student's 
t-distribution. In column two, an "NC" indicates the absence of any 
distinct maximum in the population of calculated cross-correlation 
coefficients; an asterisk indicates a "one-event" correlation, in which 
there is minimal confidence of physical reality. The error estimate in 
this column is a subjective figure derived from . the fact that a number 
of coefficients for adjacent values of At have nearly the same value. 
In column three, a negative value for At indicates that the optical 
events lead the radio events, while a positive value indicates that the 
radio events precede the optical. The error estimate here is derived 
by estimating the half-amplitude width of the distribution of correlation 
coefficients about the maximum value. 

In all the plots of R vs At that follow in this chapter, the top 
curve illustrates the relation for the raw data or "hole technique" -while 
the bottom curve illustrates the relation for interpolation across holes 



74 



75 



TABLE 4 
SUI4M/\RY OF RESULTS OF THE LINEAR CROSS-CORRELATION ANAl.YSIS 

Source R At in years N Confidence 

OJ 287 0.85+.02 -0.875+1.0 24 >99% 

OJ 287 Pt I 0.90+.03 -0.60+0.85 13 >99% 

OJ 287 Pt II 0.92+.04 0.0+0.70 15 >99% 

3C 454.3 0.79+.01 -1.2+1.2 31 >99% 

BL Lac NC(?) -0.5 (?) 

CTA 26 0.82+.08* -1.1+0.9 16 >99% 

PKS 0405-12 NC 

PKS 0420-01 0.65+.10* -0.2+0.8 16 >98% 

3C 120 HC 

NEAO 190 m 

PKS 0458-02 NC 

3C 138 NC 

PKS 0735+17 0.71+.02* +0.88+0.9 13 >99% 

PKS 0736+01 NC 

01 363 NC 

OK 290 NC 

3C 273 NC 

PKS 1354+19 NC 

OQ 208 NC 

1510-08 NC 

NRAO 512 0.66+O.lA 0.0+0.3 27 >99% 

3C 371 0.55+0.1 0.5+0.8 29 >99% 

3C 446 NC 

PKS 2345-16 NC 



in tha raw data. Except for this difference, all parameters used in 
obtaining the top and bottom curves are identical. I-Jhile both curves are 
included for completeness, all quoted values of R and At refer to the top 
curve unless explicitly stated otherwise. 

OJ 287 

This object provided the best visual correlation of all the sources 
studied in this work, a result that was strongly reinforced by the 
analytical study. Despite gaps in the optical record, there is a strong 
suggestion that the optical and radio cur-'/es shown in Figure 16 follow 
each other quite closely through a number of distinct details defined by 
each record; and in fact, there is no question that both records show a 
long-term rise and fall from 1970.0 to 1974.0 and a short-term burst 
centered at about 1975.0. Despite violent short-term optical flickering 
this visual correlation is supported both by the cross-correlation coef- 
ficient of 0.85 indicated in Figure 17, and by the relationship between 
radio flux and optical magnitude revealed in Figure 18. (The anti- 
correlations occuring in Figure 17, for large positive and negative 
values of At result naturally from the superposition of the ascending 
radio curve on the descending optical curve and vice versa.) 

Close examination of the data shows that after the gap in both 
records at 1972.75, there is more complete optical coverage and a differ- 
ent separation between the optical and radio curves than before that date, 
implying that some shift in the relationship may have occurred. This 
perception suggested a separation of the data into two segments. Part 1 
containing the data prior 1972.75 and Part II containing the data after 
1972.75. While the application of the cross-correlation technique 



77 



O 

cvi 



O 



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(X) 

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IT) 



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c u 
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V 



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a = 


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0.5 



OJ 287 



R 0.0 



9 « 



-0.5 



• • 



• a 



« « 



0.5 



R 0.0 



® 9 iX> 



-1.0 



± 



-4.0 -2.0 0.0 2.0 4.0 

At (years) 

Fissure 17. OJ 287. Normalized cross-correlation coefficient (R) vs 
time shift (At) for the radio and optical data presented in Figure 16. 
using actual data (top) and interpolated data (bottom) , with 
At-, = At = 0.12 5 year. 



79 



10.0 



8.0 



6.0 



X 



OJ 287 



o 
o • 



9 O * « • 

« • » o 

o • 
««o * • 
oo 



4.0 



2.0 



0.0 



o 



• o 
o • o • 



• o * * o 



» « « 

« • * • 



16.0 



14.0 
MAGNITUDE 



12.0 



Figure 18. OJ 287. Radio flux vs optical magnitude for At = -0.875 
vear, At = 0.05 year. Open circles represent actual data; filled 
circles represent points for which the flux or the magnitude, or both, 
have been obtained bv linear interpolation across gaps in the data. 



80 



yielded R values of 0.90 and 0.92 for Parts I and II (Figures 19 and 20) 
respectively, the smaller number of data points used in the calculations 
combined with significant edge effects, cause one to view the results 
from Parts I and II with caution. In spite of these reservations, the 
regression plots of flux vs magnitude for Parts I and II shotm in Figures 
21 and 22 display considerably less scatter than Figure 18, tending to 
support the validity of the separation of the data at 1972.75. Moreover, 
the reader should not be misled by the apparently much broader peaks 
illustrated in Figures 19 and 20 relative to the peak in Figure 17; for 
Figure 17 has a compressed time scale on the x-axis. 

3C 454.3 

Although optical data from the Rosemary Hill, Yale, and Royal 
Greenwich Observatories were used to study this source, the overlapping 
records reinforced one another when appropriate zero-level offsets were 
applied. The correspondence and mutual reinforcement are illustrated in 
Figure 23, where the three data records are displayed independently v;ith 
no zero-level offsets. This reinforcement justifies the deletion of the 
Yale data record from Figure 24 where the density of Yale data points 
xTOuld have obscured the long-term optical trends. 

Visual inspection of the radio and composite optical data illustrat- 
ed in Figure 24 indicates that while there is not as obvious a correspon- 
dence between radio and optical activity as there is for OJ 287, the radio 
and optical records show comparable variations which may be correlated. 
Application of both the "hole" and the interpolation techniques, using 
all three optical data records, yielded maximum correlation coefficients 
of 0.79 and 0.83, respectively, for the optical leading the radio by 



81 



1.0 

0.5 

0.0 

-0.5 



OJ 287 



-1.0- 
1.0 

0.5 

0.0 

-0.5 

-1.0 



-2.0 



• ••• • 



0.0 
At (years) 



1.0 



2.0 



Figure 19. OJ 287. Normalized eross-correlation coefficient (R) vs 
time shift (At) for radio and optical data prior to 1972.75, using 
actual data (top) and interpolated data (bottom) , with At^ = At^^ = 
0.05 vear. 



82 



1.0 



f 



« • ■ » I 



• • • • 



OJ 287 



).5 



R 0.0 



-0.5 



-1.0 
1.0 



0.5 



I • ••• « « 



-0,5- 



-1.0 



-2.0 



1.0 



At (years) 



2.0 



Figure 20. OJ 287. Normalized cross-correlation coefficient (R) 
vs time shift (At) for radio and optical data after 1972.75, using 
actual data (top) and Interpolated data (bottom) , V7ith 



At, = At, = 0.05 year. 
1 j> 



83 



10.0 



OJ 287 



8.0 



e « 



6.0 



X 



4.0 



o • 

» » 



• o 
o o 



o 
o 



2.0 



0.0 



16.0 



14.0 
MAGNITUDE 



12.0 



Figure 21. OJ 287. Radio flux vs optical magnitude prior to 1972.75 
for At = -0.06 year, At = 0.05 year. Open circles represent actual 
data; filled circles represent linearly interpolated data. 



10.0 



X 



8.0 



6.0 



4.0 



2.0 



0.0 



84 



OJ 287 



o 



« 9 



a « 



o 



o o 



• o o« 

« e « 

• «0 

• • • 

• o 



16.0 



14.0 



MAGNITUDE 



12.0 



Figure 22. OJ 287. R.adio flux vs optical magnitude after 1972.75 
for At = 0.0 year, At]_ = 0.05 year. Open circles represent actual 
data; filled circles represent linearly interpolated data. 



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Figure 24. 3C 454.3. Optical and Algonquin 2.8-cm observations. The optical record consists 
of Royal Greenwich B magnitudes (with a -0™47 offset) from 1966 to 1972.75; Rosemary Hill photo- 
graphic (m„„) magnitudes (with no correction to B magnitudes) from 1968.9 to 1971.5; Rosemary 
Hill B magnitudes from 1971.6 to 1975.9. Yale B magnitudes (with a +0?125 offset) from 1967.6^ 
to 1971.0 reinforce the illustrated optical activity but are not included due to the high density 
of points. The numbering of events does not imply a one-to-one correlation between corresponding 
numbers (see text) , 



15.0 



^16.0 

3 



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OPTICAL 



18.0 



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J I L L 



1966.0 67.0 68.0 69.0 70.0 



71.0 
DATE 



72.0 73.0 74.0 75.0 76.0 



a; 

00 



Figure 10. Observed optical and near- infrared spectra of selected quasai-s plotted as a 
function of rest frequency Vq = v(l+z). Standard deviation error bars ;ire indicated for 
the infrared photometry and for all spectral scanner observations where the standard devi- 
ation in log f^ is greater than 0.02. Note that Ton 256 and PHL 938 are radio quiet. 
Reproduced from Oke e_t a_l. (1970) with permission of the authors and The Astr o physical 
Jo urnal , which is published by the University of Chicago Press. 



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Figure 11, A continuation of observed optical and near- infrared spectra of selected quasars 
begun in Figure 10. Note that the visual and infrared measurements for both 3C 279 and 
3C 345 show variability. The inconsistency betv/een the spectral scanner data and the UBV 
measurements for PHL 658 is unresolved and probably instrumental. Reproduced from Oke et^ al. 
(1970) with permission of the authors and The Astrophysical Journal , X\fhich is published by 
the University of Chicago Press. 



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Figure 12. A continuation of Figure 10. Note that while 3C 454.3 and 3C 446 exhibited 
variations in the visual, infrared photometry was not obtained to check for variability. 
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Fitfui'e 13. 



3C 3A.5, 3C ■X'i6, 3C 454.3. ContinLnim nieasurcmenl:s of Lht; opcic.a.l fXix [iloLted ngaj.usc rest Pre- 



qiieucy v.^ = v(.l,4-z) l:"or dif l:eri;nt: days. Indicating ciiange of power .law index. Straiglit Jines reivrpseat 

least sr[uart'.s fits fLir a.1.1 continnuin |)(i,ints. Circled uo.ints repn-escnt emissi.on Jines. Reproduced from 

Visvanathan (1973a) w.i.tli perm Ls.s.i en of the author and 'j^il^ As tro[iJiy.siA'^l Jonrna.l . wiiicli is iiuhlislnul by tlie 
University of Cliicagi.i Press. 



Cn 



89 



approximately 1.2 years, as illustrated in Figure 25. As a check, 
application of the same procedures to the Rosemary Hill - Royal Greenwich 
composites yielded similar correlation coefficients values of 0.78 and 
0.83 for approximately the same time delay, as illustrated in Figure 26. 

Close inspection of the raw data nevertheless necessitates a 
cautious approach to the physical reality of a cross-correlation, because 
the optical data show at least four and possibly seven events depending 
on one's criterion (event 6 of the peaks numbered in Figure 24 is defined 
by a single point with a large error, and event 7 is a shallow rise and 
.fall), while the radio record suggests only four events (three major 
events with a shoulder centered on 1973.25). In addition, superposition 
of the radio and light curves with a time shift of 1.2 years does not 
bring about an exact alignment of the radio and optical events. 

In Figure 25 the extended maximum in R beginning with the radio data 
leading the optical by about three years starts with the superposition of 
radio event 1 over optical events 3 to 6, and continues as radio event 1 
passes through several optical features. This maximum has doubtful 
significance because it is a variation of the one-event correlation and 
the R vs At plot quickly deteriorates into the appearance of an edge 
effect. 

The rec-ression plot for At = -1.2 years seems to indicate a weak 
functional relationship between the optical magnitudes and radio flux, 
which is illustrated in Figure 27 for At-^ = 0.1667 years, and in Figure 
28 for At = 0.1 years. 

In an attempt to investigate whether or not the dominant radio flare 
from 1966.5 to 1970.0 is actually the cause of a spurious correlation, 
all three optical records were correlated with the Algonquin data 



90 



0.5 



R 



3C 454.3 



-0.5- 



-1.0 
1.0 



1.5^ 



R 0.0 



-0.5 



-1.0 



• •• • . 


• 

• 

• 
• 

1 1 1 1 1 1 1 



-6.0 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



6.0 



Figure 25. 3C 454.3. Normalized cross-correlation coefficient (R) -vs 
tirae shift (At) for the optical and radio data presented in Figure 24, 
including the Yale Observatory data, using actual data (top) and inter- 
polated data (bottom), with At = At = 0.1667 year. 



91 



1.0 



0.5L 



R 0. 



-0.5- 



1 1 1 



* • 

« « 

• 

a 
• 
a 

• 
• 


1 i 1 1 

3C 454.3 
. . « . • 

• * • * 

« 
• • — 

• c a 

9 


o » 

• « 
« a 

! 1 1 


1 ! 1 ! 



R 




0.0 
At (years! 



Figure 26. 3C 454.3. Normalized cross-correlation coefficient (R) vs 

time shift (At) for the optical and radio data presented in Figure 24, 

excluding Yale Observatory data, using actual data (top) and inter- 

Dolated data (bottom), with At, = At = 0.1667 vear. 

13 



92 




19.0 



17.0 
MAGNITUDE 



Figure 27. 3C 454.3. Radio flux vs optical magnitude using all 
the optical and radio data, with At = -1.2 year, At^ = 0.1667 year, 
Open circles represent actual data; filled circles"^represent 
linearly interpolated data. 



40.0 



30.0 



X 



20.0 



10.0 



0.0 



3C 454.3 



o • 
•o • *o 



o 



oo 
o 



O 'O 

oo o 
•ooo o 
«oooo o o 

CO 
o • 



19.0 



17.0 
MAGNITUDE 



15.0 



Figure 28. 3C 454.3. Radio flux vs optical magnitude using all 
the optical and radio data, with At = -1.2 year, At^ =0.1 year. 
Open circles represent actual data; filled circles represent 
linearly interoolated data. 



94 



obtained after 1970.0. While the resultant R vs At diagram illus- 
trated in Figure 29 has a much narrower peak of R = 0.63 at a At of 
about -1.2 years than does Figure 25, the two plots are quite similar. 
Both plots show the same general character for -6.0 < At < +0.0; for 
At > 3.0 years, Figure 29 deteriorates into the edge effect suggested 
by the top half of Figure 25 for At > 4.0 years; however, the character 
of the two plots is quite different for 0.0 < At < 3.0 years. 

Since both the radio and optical records show comparable activity, 
the similarity between Figures 25 and 29 is not really surprising. 
When one considers that by deleting the radio data prior to 1970.0, 
approximately a third of the radio data have been ignored, the deteri- 
oration of the analytical correlation for this case cannot be given 
much weight . 

As a check of the analytical correlation procedures, the Dent 
1.9-cm and Algonquin 2.8~cm radio curves illustrated in Figure 30 were 
correlated, with the higher-frequency 1.9-cm data assuming the role of 
the optical record. The results plotted in Figure 31 indicate a 0.97 
correlation coefficient for the 1.9-cm data leading the 2.8-cm data by 
approximately 0.1 year, which is the qualitative result expected from 
the simple expanding source model. The long decline in the value of 
R from At = 0.5 to 3.0 years is most likely the result of a combination 
of the lack of 1.9-cm data corresponding to the first dominant 2.8-cm 
flare and the varying alignment of that dominant 2.8-cm flare with the 
smaller 1.9-cm flares from 1970.5 to 1974.-5. 



95 



R 0.0 




R 0.0 



-2.0 0.0 2.0 

At (years) 



Figure 29. 3C 454.3. Normalized cross-correlation coefficient (R) 
vs time shift (At) for all the optical data but only the radio data 
obtained after 1970.0, using actual data (top) and interpolated 
data (bottom) with At = At = 0.1667 year. 



Ar 



CSD 






CO 



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- CO 



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to 

CO 






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r-- 




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i i 1 " 

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e 


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9 <9 
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e 

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0.0 

At (years) 



Figure 31. 3C 454.3. Normalized cross-correlation coefticient (R) vs 
time shift (At) for the two radio records of Figure 30, using actual 
data (top) and interpolated data (bottom), with At = At = 0.1 year. 



93 



BL Lac 

Examination of the optical and radio curves in Figure 32 indicates 
no obvious overall correlation except that both show numerous, similar 
rapid events on a time scale of months. The plot of R vs At in Figure 
33, for At = At = 0.1667 years, superficially resembles a scatter 
diagram, but it nevertheless shows a general trend toward a maximum 
centered at about At = -0.5 year that may be indicative of a long-term 
correlation that is obscured by the almost incessant flickering. 

The unusually short time scale of the variability, coupled with 
the unavoidable gaps in the optical data, make BL Lac difficult to 
analyze in a definitive manner. It should also be emphasized that the 
analysis attempted thus far is merely a linear correlation; the trend 
toward a maximum in Figure 33 may indicate that a different, non-linear 
relationship exists which would be sharpened by the appropriate type 
of analysis. 

Finally, it should be noted that the choice of At^ and At„ used 
to obtain Figure 33 was not based on the criteria reviewed earlier, but 
rather on the basis of what values seemed better to illustrate the 
trend towards a maximum correlation coefficient. The time resolution 
of the data actually supports values of At^ = At^ = 0.0625 years, which 
were used to obtain Figure 3A. Vlhile these latter plots have many more 
points, the general character of the R vs At relation does not differ 
between Figures 33 and 34. 



99 



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100 



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At (years) 



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vs time shift (At) for the optical and radio data presented in 
Figure 32, using actual data (top) and interpolated data (bottom), 
with At, = At = 0.1667 year. 



1.0r 
0.5 



BLLAC 



R 0.0 

-0.5 
-1.0 

1.0r 

0.5 

R 0.0 

-0.5 

-1.0 



6.0 



-4.0 



-2.0 



0.0 

At (years) 



2.0 



4.0 



6.0 



Figure 34. BL Lac. Normalized cross-correlation coefficient (R) 
vs time shift (At) for the radio and optical data presented in 
Figure 32, using actual data (top) and interpolated data (bottom), 
with At = At = 0.0625 year. 



o 



102 



CTA 26 (PKS 0336-01) 

A preliminary examination of Figure 35 suggests little correspon- 
dence between the optical and radio data, but the cross- correlation 
analysis results illustrated in Figure 36 show a distinct maximum for 
a radio time lag of about one year. Closer examination of the optical 
data reveals that if one averages points, there is a roughly 2.0- to 
2.5-a bump between 1970.0 and 1972.75 that correlates with a major 
radio event centered at 1972.2. If the correlation is real it would 
mean that, although the event happened later at radio wavelengths, both 
the radio intensity and the optical intensity (not optical magnitude) 
rose by the same amplitude (a factor of 1.8 above the "base" level), 
but the radio peak probably had a smaller half-width. This is in con- 
tradiction to what one would expect from a naive extrapolation of the 
simple expanding source model. 

Regression plots for At = 0.0 and -1.125 years, Figures 37 and 38, 
indicate that there is a tighter grouping of points and therefore a 
better defined flux to magnitude relationship for the latter value of 
At; but this is simply a result of the apparent correlation indicated 
in Figure 36. The entire correlation is of course a "one-event" 
correlation and is unimpressive because of the relative lack of activity 
at optical wavelengths - 

PKS 0405-12 
Figure 39 shows little significant optical or radio structure 
except for the peculiar change in radio level at approximately 1969.6. 



17.0 



UJ 
Q 

^18.0 

CD 



19.0 



OPTICAL 



RADIO 

J III 



ll |l 



H 



I 



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ir ri 



1 



J I I I I L 



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llll 



li 



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1967.0 68.0 



5.0 



4.0 






3.0 



2.0 



69.0 70.0 71.0 ^„^^ 72.0 73.0 74.0 75.0 76.0 

DATE 



Figure 3.5. CTA 26 (PKS 0336-01). Rosemary Hill photographic 
magnitudes and Algonquin 2.8-em observations. 



o 



].5 



R 0.0 



10^ 



CTA26 



» * • » 

t> 9 e • 



-0.5 



» « I 



ffi « 
« « 



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1.0 



0.5 



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4» « O O O 9 

A « e » » 



-4.0 



-2.[ 



0.0 
At (years) 



2.0 



4.C 



Figure 36. CTA 26 (PKS 0336-01). Normalized cross-correlation 

coefficient (R) vs time shift (At) for the optical and radio data 

presented in Figure 35, using actual data (top) and interpolated 

data (bottom), with At^ = At^ = 0.125 year. 

1 J 



105 




MAGNITUDE 



Figure 37. CTA 26 (PKS 0336-01). Radio flux vs optical magnitude 
for the data presented in Figure 35, with At = 0.0 years, At]_ = 



0.1 year. Open circles represent actual data; 
represent linearly interpolated data. 



filled circles 



L06 



X 



u.u 


— 


CTA26 






— 


8.0 












6.0 












4.0 

2.0 
nn 




I 


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1 1 1 



19.0 



17.0 



15.0 



MAGNITUDE 



Figure 38. CTA 26 (PKS 0336-01). Radio flux vs optical 
magnitude for the data presented in Figure 35, with At = -1.125 
year, At^ =0.1 year. Open circles represent actual data; 
filled circles represent linearly interpolated data. 



14.0r 



Q 

ID 

tis.o 

o 
< 



OPTICAL 



6,0 



RADIO 

I 



± 



l___™-i- 



19670 68.0 



+ + 
+ 



4i 



+ -fH + 



+ + 



I M 111 I I It I HI J I 



1 L 



69.0 



70.0 
DATE 



71.0 



72.0 



3.0 



2.0 



>- 



1.0 



.J___J- 



73.0 



74.0 



Figure 39. PKS 0405-12. Royal Greenwich 

B magnitudes and Algonquin 2.8-cm observa Lions. 



I--' 
o 



108 

The top half of Figure 40 thus gives a good example of the results of 
the correlation technique when too small a data sample is used, while 
the bottom half of the same figure illustrates that the interpolation 
technique can synthesize an apparently well-behaved R vs At relationship 
even when there is too little data. 

PKS 0420-01 
There is no apparent visual relationship between the optical and 
radio records displayed in Figure 41. If the Rosemary Hill optical 
magnitudes are correlated only with the Dent 1.9-cm record which begins 
in 1969.7, the results in Figure 42 are rather uninteresting with no 
clearly defined maximum. However, if the 1-9-cm record is supplemented 
with the Algonquin 2.8-cm record from 1967.5 to 1969.6, a relatively 
clearly defined maximum correlation (0.65) is established for the 
optical leading the radio by 0.2 year, as seen in Figure 43. Super- 
position of the radio and optical records indicates that this is most 
likely due to some limited corresponding trends in both records. To 
date no definite radio counterpart to the conspicious optical flare at 
the end of 1974 has emerged; however, the latest 9-mm observation by 
Dent (1976) indicates a possible significant increase. He has not seen 
any increase at 1.9 cm as of this writing. 

3C 120 
Figure 44 shows variations on a time scale of approximately one- 
half year in both the radio and optical data, but neither visual inspec- 
tion nor the results of the correlation analysis in Figure 45 yield any 
significant correlation. The problem here is not dissimilar to that of 



109 



1.0 

0.5 

R 0.0 

-0.5 

-1.0 
1.0 

0.5 

R 0.0 

-0.5 
-1.0 



i 1 1 I -^ 

0405 - 12 
• • 

• 
• 


• • 

— • • • t . _ 

• 

• 
• 

• • 

• 

I ' 1 1 1 1 



-4.0 



-2.0 







2.0 



4.0 



At (years) 



Figure 40. PKS 0405-12. Normalized cross-correlation coefficient 
(R) vs time shift (At) for the optical and radio data presented in 
Figure 39, using actual data (top) and Interpolated data (bottom). 



with At. 



At, 



0.1 year, 



Figure 41. PKS 0420-01. Rosemary Hill photographic magnitudes and radio flux. 
The radio record consists of Algonquin 2.8-cm data from 1967.7 to 1969.7 and 
Dent 1.9-cm data from 1969.7 to 1975.5; the dashed vertical line indicates the 
transition between the two sets of data. 



17.0 



Q 

1 18.0 



19.0 



OPTICAL 



kki\ 



■\ 



h 



't'||',i; 



RADIO 



J__ 1 \ __i„ 



i 1 



I M^Mu^^ l.+ i ^ t 



I 



J 1 _1__._L 



.1 L 



3.0 



2.0^ 



.0 



1968.0 69.0 70.0 



71.0 72.0 73.0 74.0 

DATE 



75.0 76.0 



112 



1.0 



0.5- 



-0.5- 



1 • 

• 

• 
« 

• 


* 


• 

* e, 

• • • 

• 

• • • 

• 

• 


1 1 1 

0420 - 01 

• • • . 

« • • 

• 

• • 

' ' * • . • • . - 

. . . 

• . • • • 

• • • 
• 

• 

• • 


• 

1 

t. -i.. 


o 

• 

« 
• 


• « 

1 


• 

1 1 1 




0.0 
At (years) 



4.0 



Figure A2, PKS 0420-01. Normalized cross-correlation coefficient 
(R) vs time shift (At) for all the optical but only the Dent 1.9-cm 
data in Figure 41, using actual data (top) and interpolated data 
(bottom), with At, = At = 0.1 year. 



113 



1.0 

0.5 



-0.5 



-1.0 



R 0.0 



-0.5 



-1.0 



0420 - 01 



•• • 



1.0 r 



0.5 



-4.0 



••••••• 



-U 



0.0 
At (years) 



2.0 



4.0 



Figure 43. PKS 0420-01. Normalized cross-correlation coefficient 
(R) vs time shift (At) for all the optical and radio data presented 
in Figure 41, using actual data (top) and interpolated data (bottom), 
with At = At =0.1 year. 



Figure 44. 3C 120. Optical and Algonquin 2.8-cm observations. The optical record consists 
of Klnman (1968) B magnitudes from 1967.1 to 1968.1; Royal Greenwich B magnitudes from 
1967.9 to 1970.2; Rosemary Hill photographic magnitudes (corrected to B magnitudes) from 
1969.9 to 1971.7; and Rosemary Hill B magnitudes from 1971.8 to 1975.9. Both the Kinman and 
the Royal Greenwich B magnitudes were reduced with a Kinman sequence and have been plotted 
with an offset of -0™125. Rosemary Hill used a combined sequence from Kinman (1968) and 
Angione (1971) . 



!4.0 



OPTICAL 



UJ 
Q 

I' 

CD 
< 

5 



*^i 



n 



5.0 



+ 



16.0 



+ 
+ 



It 



H 



tH: 



fe 



fe 



•f, lit 



RADIO 



1^1 n 



^i 



11^ i 



* ^^* V^.,^ ..I *^^iHi 






I 



( 



I 



+\ 



H4 f |l%. 






— ' -J— ' i ! J 1 1 \ 1 I I I I ■ I I 



18.0 



12.0 



>- 



6.0 



1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74 75 760" 

DATE ■ 



\ 



Figure 45. 3C 120. Normalized cross-correlation coefficient (R) vs time shift (At) for the 
optical and radio data presented in Figure 44, using actual data (top) and interpolated data 
(bottom), with At = At„ = 0.0833 year. 



R 



1.0 
0.5 
0.0 

-0.5 

-1,0 

1.0 

0.5 

R 0.0 

-0.5 

-1.0 



1 1 


• 


1 1 1 1 1 

3C 120 

• 9 ~ 


• 
• 
•• 

• 

9 

• 

• 

1 1 




• •• • " "... • '. •• . .. • • .. ''. ' 

«• • • _ 

• • 

1 1 1 1 1 



» »• 999 



• -•••••a 



• a 



•6.0 



4.0 



-2.0 



0.0 
At (years 



2.0 



4.0 



6.0 



1-' 



118 



BL Lac, in that a multitude of brief events creates so many potential 
correlations that none is convincing. However, the values of R for 
3C 120 do not even show a trend toward a maximum which appears to exist 
in BL Lac. 

■ NRAO 190 (PKS 0440-00) 

The record of optical and radio data in Figure 46 as yet exhibits 
no radio counterpart to the approximately 1. 5-magnitude drop and sub- 
sequent violent optical flare observed between 1972,75 and 1976.0, nor 
any obvious visual relationships between the two sets of data. The 
cross-correlation calculations are similarly uninteresting, exhibiting 
no significant maxima. This is illustrated in Figure 47 where only the 
Dent 1.9-cm radio data was used, and in Figure 48 where the 1.9-cm data 
record was supplemented by Algonquin 2.8-cm data from 1966.9 to 1969.0. 
Again these last two figures give an indication of how the R vs At olots 
change as more data are used. 

Clearly it would be of interest if the 1976 radio observations 
reflect the unusually sharp optical spike in late 1975, but as of 
June 28, 1976, Dent (1976) has seen no significant increase in the 
1,9-cm flux level, 

PKS 0458-02 
In Figure 49, the relatively sparse and featureless optical data 
show no counterpart to the double radio flare centered at 1972.75. The 
R vs At plot for the hole technique, displayed at the top of Figure 50, 
has the scatter diagram appearance characteristic of an insufficient 
number of data points; however it is of interest to note that the bottom 



17.0 



LiJ 
Q 

H 

o 



OPTICAL 



8.0 



19.0 



li 



|l tl' l' (l| 



RADIO 



III! 



'\ I t. , 



\\ 



i^w ^;* 0^ u 



M^^ 



i** i I * 



.0 



2.0 



^ 



.0 



J I L 



J I L 



J L 



1967.0 68.0 



690 70.0 



71.0 72 

DATE 



73.0 74.0 



750 



760 



Figure 46. NRAO 190 (PKS 0440-00). Rosemary Hil.l photographic magni- 
tudes and radio flux. The radio record consists of Algonquin 2.8-cm 
data (offset by -0.3 Jy) from 1966.9 to 1969.8, and Dent 1.9-cm data 
from 1970.0 to 1975.5; the dashed vertical line indicates the transi- 
tion between the tv/o sets of data. 



120 



0.5 



R 0.0 



-0.5 



-1.0 
1.0 



0.5 



R 0.0 



-0.5 



-1.0 



-6.[ 



NRAO 190 



O 9 9 






-4.0 



-2.0 



0.0 
At (years! 



2.0 



4.0 



6.0 



Figure 47. NRAO 190 (PKS 0440-00). Normalized cross-correlation 
coefficient (R) vs time shift (At) for all the optical data but 
only the 1.9-cm radio data presented in Figure 46, using actual 
data (top) and interpolated data (bottom), vrith At =At =0.1667 year 



121 



1.0 



0.5 



R 0.0 



-0, 



-1.0 
1.0 

0.5 h 



R 0.0 



-0.5 



-1.0- 



- <> — o ♦ a 



NRAO 190 



« • • 



-6.0 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



6.0 



Figure 48, NRAO 190 (PKS 0440-00). Normalized cross-correlation 
coefficient (R) vs time shift (At) for all the optical and radio 
data presented in Figure 46, using actual data (top) and inter- 
polated data (bottom), with At = At^ = 0.1667 year. 



18.0 



UJ 
Q 

< 



9.0 



20.0 



OPTICAL 



t 1 



It 



RADIO 

il 



t 



t^ 



i I t'l| I 



HlfVllnl 



,i"'„«"' 



11 



It 



it 



J... I _j- 



I I I I I I L__ J- 1 L 

1968.0 69.0 70.0 71.0 72.0 73.0 74.0 

DATE 



h 



I'M 



3.0 



2.0^ 



1.0 



75.0 



76.0 



Figure 49. PKS 0458-02. Rosemary Hill photographic 
magnitudes and Algonquin 2.8-cm observations. 






I.U 


1 


1 


1 1 
0458 - 


02 


1 1 

ft 


0.5 


■ 


• 


• 
• • 
• 
• • 


• 


ft ft ♦ — 

• ft 


R 0.0 
-0.5 


• 


ft 


• ft 

• ft • • 


• • 
• 


• 
ft • 
• ft 


- 


• 

• 
ft 
• • • 

• 
• 

• 
ft 


ft 
• 

* 

• • 
* 

ft 

• 
• 


• • 
• 


• 

ft • 

ft ft 

• m 
• 


-1.0 


""i 


• 

1 


1 1 




ft — 

1 1 



I.U 








0.5 


- 


ft 

.. 

ft 
ft ■ 

• 

ft 


• 

• 

• 


R 0.0 
-0.5 




. 


ft ft 




ft 

• 
* ft «• 
ft . ft ft • ft 
• • « ft«» 

• •ft ft • • '%• 

• 

• ft ■ • 

• ■ 


ft 

• ft 
• 

• 

ft 

ft 
ft 






ft • • 
ft 

ft 




-1.0 


1 


1 1 1 1 


1 1 




B.0 


-4.0 -2.0 0.0 2.0 


4,0 6.0 



At (years) 

Figure 50. PKS 0458-02. Normalized cross-correlation coefficienL (R) 
vs time shift (At) for all the optical aud radio data presented in 
Figure 49, using actual data (top) and interpolated data (bottom), 
with At = At = 0.125 year. 






12.4 



half of Figure 50, resulting from the interpolation technique, has mold- 
ed the sparse data into an apparently well-behaved R vs At relation, 
with a maximum correlation coefficient of 0.63 at a At of -1.0 years. 
This is most likely a spurious result caused by the sparse sampling of 
the optical activity and resultant similar trends between the optical 
and radio records. While it is possible that the correlation indicated 
by the interpolation technique is real, it will require a higher time- 
resolution documentation of optical activity to establish the validity 
of such a correlation. 

3C 138 (PKS 0518+16) 
An examination of Figure 51 indicates that there is little data 
overlap for any correlation investigation, except in the highly unlikely 
case that the radio leads the optical. Moreover, the optical observa- 
tions show considerable activity xvhile the radio record is nearly 
featureless. The analytical correlation again shows a scatter diagram 
for the hole technique and an apparently well-behaved R vs At relation 
resulting from the interpolation technique, as shown in Figure 52. The 
maximum correlation coefficient of 0.70 determined from the interpola- 
tion technique is based on only seven radio measurements that indicate 
a slight rise that coincides with the optical event centered at 1972.0, 
for a At of -1.1 year. This then could be considered a weak one-event 
correlation. The secondary maximum of 0,60 at a At of +1.0 year uses 
more radio data, but there is a gap in the radio coverage during the 
optical flare centered at 1974.0. Thus more radio data will need to be 
included in the analysis before any significance can be given to the 
results of the interpolation technique. 



18.0 



u 
a 

CD 



9.0 



200 



OPTICAL 



I 



It 



i II 



111 



RADIO 



(it lH''''t|'l III '|l 11 I 'i „ll I I 'I'll 



3,0 



2.0 






1967.0 68.0 69.0 



J I 1 I I 



70.0 71.0 72.0 

DATE 



J L 



73.0 74.0 75.0 76.0 



1.0 



Figure 51. 3C 138 (PKS 0518+16). Rosemary HJ 11 photo- 
graphic magnitudes and Algonquin 2.8-cm observations. 



ISO 



Figure 52. 3C 138 (PKS 0518+16). Normalized cross- 
correlation coefficient (R) vs time shift (At) for the 
optical and radio data presented in Figure 5]., using 
actual data (top) and interpolated data (bottom), with 
At = At = 0.125 year. 



1.0 

0.5 

R 0.0 

-0.5 



-1.0- 



i 


1 - 1 . 1 1 1 1 

3C 138 




ft ft 
ft " • 

ft * 


— 


ft , •• - 




ft • ft 




ft 
ft ft ft ft , 

• ft 

• ft ft 




. . • • • •• 
... . . 




ft 
• ft 




• ••. 




ft 
• • 


~ 1 


ft ft ft* — 

1 1 1 II 1 




0.0 
At (years) 






128 



PKS 0735+17 

Figure 53 displays the full 1.9- and 2.8-cm data records, which 
were analytically correlated as a test of the correlation procedures. 
The resulting R vs At plots are shown in Figure 54, where the correlation 
coefficient reached a maximum value of 0.91 at At = -0.125 year for both 
the hole and the interpolation precedures. 

The optical and composite radio records illustrated in Figure 55 
show optical variations on a very short time scale, whereas the radio 
variations appear more as gentle, long-term undulations. For a complete 
study, the optical record was analytically correlated first with the 
2.8-cm record. The results plotted in Figure 56 are not very convincing 
due to the scatter, the suggestion of a double maximum, and the relative- 
ly low value of the maximum correlation coefficient which reaches a 
value of 0.52 at At = -rO.5 years and At = -0.4 years for the hole and 
interpolation procedures respectively. However, it should be noted that 
the 2.8-cm record stops at the beginning of a long 2-year rise document- 
ed in the optical and the 1.9-cm records. 

Next the 1.9-cm record was correlated with the optical record, with 
the results plotted in Figure 57. In this case, the maximum correlation 
coefficient reached a value of approximately 0.71 at At = 0.9 years and 
0.59 at At = 0.7 years for the hole and interpolation procedures 
respectively. 

Finally, the results from correlating the optical record with the 
composite 1,9- and 2.8-cm record are presented in Figure 58, where the 
maximum coefficient reaches values of approximately 0,72 ac At = 0.9 
years and 0.60 at At = 0.7 years for the two techniques. 



3.0 

^ 2.0 

1.0 



0735 + 17 



^ ^ Ml 



S h K 
S f ^ w ^ 






t ^ 'f 



it.? 



it 



Ht ti 



Kk) '* (I 



ft|i,i,;(\ttt*)«r"ts 



t|'M|fl|H I I I 1) 



l( 



3.0 



2.0 



1.0 



>- 



1967.0" 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 7B.0 

DATE 



Figure 53. PKS 0735+17. Dent 1.9-cm observations 
(top) and Algonquin 2.8-cm observations (bottom). 



ho 



130 



1.0 

0.5 

R 0.0 

-0.5 



1 1 .1 1 1 

0735 + 17 

• • • 

« 

• •- 
•• 

•• 


• 
• 

• 

• 

• 
• • • 

- . . . • • • - 

• • • 
• • 

• 

1 * ' 1 1 1 1 




0.0 
Atlyears) 



2.0 



4.0 



Figure 54. PKS 0735+17. Normalized cross-correlation 
coefficient (R) vs time shift (At) for the two radio 
records in Figure 53, using actual data (top) and inter- 
polated data (bottom), with At = At = 0.125 year. 



I 4 Or 



UJI50 

Q 



2 1 6.0 



OPTICAL 



t I 



i 






17.0 



RADIO 



.til 



4i,i !' 



I, "'ii^i 



1, 'h'. 



\ ♦h i^ * 



I /<! 



3.0 



1} 



^ 'f 



2.0 



>- 



.0 



19670 680 69.0 70 710 72 73 74.0 75.0 76.0 

DATE 



Figure 55. PKS 0735+17. Rosemary Hill photographic magnitudes and 
radio flux. The radio record consists of Algonquin 2.8-cm data from 
1966.9 to 1970.2, and Dent 1.9-cm data from 1969.6 to 1975.6. The 
dashed vertical line indicates the transition to 1.9-cm data alone. 



132 



I.U 


1 




1 1 


0735 + 17 


0.5 


- 




• 

• • • 

• • * 
• • 

• 


— 


R 0.0 






• 

• 
• • 

• 

• 


• 
• 






• 
• 


* • • 

« 
* • 
* • ft 


-0.5 







• 

• • 


ft 

• 

• • ft 

• 

ft ft 






• 


9 
« 


• • • 

• 


-1.0 


1 

1 


• 
• 


4 
*• 

1 1 


1 1 



R 0.0 




-4. 



-2.0 



0.0 

At (years) 



2.0 



Figure 56. PKS 0735-M7. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for all the optical data but only 
the 2.S-cm radio data, using actual data (top) and interpolated 
data (bottom), with At, = At = 0.125 year. 



133 



I.U 
0.5 




-^ r 

• 




• « 

• 
• 


• 

« 


1 1 

0735 + 17 

• 


0.0 






• • 


• 




«0 




« 


• 
• 






• 

« 

• • 






« « 








• • • . 

• 


-0.5 


— 


• 










• • 

• • — 
« « 

« • • 


-1.0 


— 


• 
• • 

a 

1 1 




! 




a 

• 

1 1 



1.0 



0.5 



R 0.0 



-0.5 



-1.0 



•• •• • 



• * 



t e « • ft V 

• •• • • 

•• •• ■ » 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 57. PKS 0735-1-17. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for all the optical data but only the 
1.9-cm radio data, using actual data (top) and interpolated data 
(bottom), with At, = At = 0.125 year. 



134 



1.0 

0.5 

R 0.0 



0735 + 17 



-0.5 



-1.0 



L 



I.Or 



0.5 



R 0.0 
-0.5 



-1.0 



o • 



B • 



• e • 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 58. PKS 0735-1-17. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for all the optical and radio 
data in Figure 55, using actual data (top) and interpolated 
data (bottom), xvith At^ = ^t^ = 0.125 year. 



135 



While the last two R vs At plots seem to indicate a potentially 
significant correlation, it must be remembered that this correlation 
occurs for the theoretically unlikely condition of the radio leading the 
optical. This correlation is caused by the 1970.2 to 1975.2 radio 
"trough" aligning with what could be argued is a similar long-term 
optical trough about which the optical data flicker. VJhile a plot of 
1.9-cm radio flux vs optical magnitude for At = 0.8 year indicates a 
possible weak functional relationship in Figure 59, the character of the 
plot does not differ noticeably from the same plot for At = 0.0 shoxm in 
Figure 60. VJith the present data, this can probably be considered a 
"one-event" correlation, and thus less than completely convincing. 

PKS 0736+01 



Both the radio and the optical data records plotted in Figure 61 
exhibit significant activity with events in both domains on a time scale 
of the order of a year; however, neither visual nor linear analytic 
correlations could be found. It is interesting to note the change in 
character of the S. vs At plots between Figure 62, in which only the 1.9- 
cm data were used, and Figure 63, in which 2,8-cm data from 1967 to 
1970.5 were used to supplement the 1.9-cm data. The scatter in the top 
half of the figures is reduced while the excursions from zero in the 
bottom half are increased in amplitude. This latter effect is probably 
due to the greater amplitude radio flares recorded prior to 1970,5. 

01 363 
Figure 64 shows nearly featureless records for both the optical and 
the radio data, except for a possible monotic long-term optical rise of 



136 



X 




MAGNITUDE 



Figure 59. PKS 0735+17. Radio flux vs optical magnitude using 
all the optical data and the 1.9-cin radio data, with At = 0.8 
year, At]_ = 0.1 year. Open circles represent actual data; 
filled circles represent linearly interpolated data. 



137 



X 




17.0 



15.0 
MAGNITUDE 



Figure 60. PKS 0735+17. Radio flux vs optical magnitude 
using all the optical data and the 1.9-cra radio data, with 
At = 0.0 year, At]_ = 0.1 year. Open circles represent actual 
data; filled circles represent linearly interpolated data. 



Figure 61. PKS 0736+01. Rosemary Hill photographic magnitudes and radio flux. The radio data 
consists of Algonquin 2.8-cm data from 1966.8 to 1970.5, and Dent 1.9-cm data from 1970.6 to 1975.6, 
The dashed vertical line indicates the transition between the two sets of data. 



15.0 



Q 

tie.o 

CD 



17.0 



OPTICAL 






Vi 



*f, 



H 'I 



,f, 



I 1 



RADIO 



I ' y " 1 1, 






, t" 






3.0 



2.0 



.0 



>- 



J L 



J L__j L 



19670 68.0 69.0 70.0 



71.0 72.0 

DATE 



73.0 74.0 75.0 76.0 






140 



1.0 



0.5 



• • 



0736+01 






R 0.0 



-0.5 



• • 



-1.0 
1.0 



0.5 



R 0.0 



-0.5 



-1.0 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 62. PKS 0736+01. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for all the optical data but only 
the 1.9-cin radio data, using actual data (top) and interpolated 
data (bottom), with At = At = 0.125 year. 



141 



0.5 

R 0.0 

-0.5 



0736+ 01 



• • 






0.5 

R 0.0 

-0.5 
-1.0 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 63. PKS 0736-f-Ol. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for all the optical and radio data 
presented in Figure 51, using actual data (top) and interpolated 
data (bottom) , with At 



1 



At^ = 0.125 year, 



15.0 



LU 
Q 
ID 

^16.0 

o 
< 



7.0 



OPTICAL 



^tl 



A 



\ 



RADIO 



I't'll 



± 



lllll'll «|l'|l"lll I II 1, 1 1 il||i ii|l| 



± 



3.0 



2.0^ 



.0 



1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 

DATE 



76.0 



Figure 64. 01 363. Rosemary Hill photographic 
magnitudes and Algonquin 2.8-cra observations. 



N3 



143 

072 and a small wandering of the radio baseline, both of which are in 
the formal sense statistically insignificant. The R vs At plot in 
Figure 65 yields a scatter diagram for the hole technique, but with 
primarily negative coefficient values that may result from opposed 
small slopes. 

OK 290 
Visual inspection of the radio and optical records plotted in 
Figure 66 shows some evidence that the optical events characteristically 
have a shorter time scale, and reveals a possible correlation for At = 
-1.25 years that becomes easier to see when the two records are super- 
imposed on one another with that time delay. However, the family of 
calculated correlation coefficients from the hole technique, seen in 
Figure 67, x^^anders with some scatter which begins to have the appearance 
resulting from too little data. The interpolation technique results in 
clearly defined maxima of approximately R = 0.87 for the optical leading 
the radio by about 4.0 years and R = 0.62 for the radio leading the 
optical by about 1.6 years. Superposition of the radio and light curves 
indicates that the former is caused by the alignment of the 1971.0 - 
1972.0 optical rise with the 1975.0 - 1976.0 radio rise, while the 
latter is probably caused by correspondence of random trends. Thus the 
linear correlation technique offers no support for the suggested visual 
correlation. 



144 



l.U 


01 363 


0.5 


• * • • 


R 0.0 

-0.5 


« 
• 


• 

• • • « 

• . •••... 

• • • . • 


-1.0 


* • • 

1 ■ 1 1 1 1 



0.5 



R 0.[ 



-0.5 



1.0 



• • • 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 65. 01 353. Normalized cross-correlation coefficient 
(R) vs time shift (At) for the optical and radio data presented 
in Figure 64, using actual data (top) and interpolated data 



(bottom) , with At. 



At, 



0.125 year 



145 




a 


m 


CO 


S 


1-4 





M 


"n 


O 


iJ 


J-i 


rt 





> 


^ 


n 


C-^ 


(U 




m 


rH 


^ 


iH 


o 


■H 




ffi 


e 




a 


l>i 


1 


U 


CO 


W 


• 


s 


o-i 


0) 




m 


c 


n 


•H 


Pi 


;3 




cr 










> 


o 


o 


&D 


rr\ 


^ 


CN 


<C 


^ 


p.- 


O 


C 




CO 


, 


en 


v£) 


0) 


MO 


T-; 










a.) 


j_i 


u 


•H 


;3 


c 


&D 


M 


•H 


CO 


f=4 


P 



3aniiN9vi^j 



146 



1.0 



OK 290 






0.5 



R 0.0 



e 9 a 



-0.5 



-1.0 
1.0 



0.5 



R 0.0 



-0.5 



• 



» « 



-1. 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 67. OK 290. Normalized cross-correlation coeffi- 
cient (R) vs time shift (^t) for the optical and radio data 
presented in Figure 65, using actual data (top) and inter- 



polated data (bottom) , with At 



1 



ii L , 



0.125 year. 



147 



3C 273 

The full 1.9- and 2.8-cm data records presented in Figure 68 were 
linearly correlated as another test of the analytical procedures, with 
the resultant R vs At plots shown in Figure 69, where the maximum 
coefficient reaches a value of approximately 0.87 for At - -0.125 year 
for both procedures. 

The close correspondence in the character of Cent's 1,9-cm varia- 
tions with the variations recorded by Algonquin's 2,8-cm data led to the 
inclusion of 1.9-cin data from Alien et al. (1968) to show that this well- 
known source had undergone a steep rise in its radio flux in the mid- 
1960' s, as illustrated in Figure 70. Due to the lack of overlap between 
the Allen data and the other two sets, an offset of -19.0 flux units was 
applied to this early 1.9~cm data purely for the cosmetic purpose of 
matching its termination with the beginning of the Algonquin 2,8-cm 
coverage. 

After its initial steep rise the radio data shov7 variations that 
might be interpreted as roughly periodic (a very controversial topic, in 
particular for the optical record, as the literature demonstrates), and 
which are similar to the cyclic nature of the optical data. But a 
number of the later radio cycles occur during what appears to be, within 
the limits of the observations, a nearly quiescent optical era. The 
maximum cyclic amplitudes of both the radio and optical intensities are 
comparable; each increases by a factor of about 1.4. 

The calculation of the correlation coefficients using only the 
Algonquin 2.8-cm data, or the Algonquin 2.8-cm data and the Dent 1.9-cm 
data, yields a spurious one-event maximum due to the alignment of the 
1966,7 to 1969.5 radio trough with the 1968,0 to 1971.3 optical trough, 



145 



Ar 



CD 

CO 



CD 
CD 



CO 
CsJ 

CO 



-^^4;p^ 



CO 



LO 



"<J 



CO 

CO 






<3: 

CD 



CO 
CO 



oo 

CO 



CO 

CO 
CO 



CO 

CO 



CO 
CO 
CD 



CO 
CO 



AP 



CO 
CO 



o 



o 


. 


•H 


^--^ 


J_l 


e 


01 


o 


s> 


ij 


M 


4-1 


OJ 





m 


r> 


^ 


Vw^ 









« 


S 


c 


o 


o 


1 


•H 


CT> 


JJ 


• 


Cit 


>H 


> 




u 


J-J 


0) 


H 


M 


CU 


rQ 


c 













• 


U 


c^ 


; 


t~~ 


CO 


c^ 


■ 




CN 


U 




ro 


r^ 




•H 










• 


cr 


00 




o 







(K) 


OJ 


rH 


!-i 


< 


D 




M TJ 


•r-f 


c 


f^ 


nj 



Figure 69. 3C 273. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for the radio data presented 
in Figure 68, using actual data (top) and interpolated 
data (bottom), with At^ = At„ = 0,0833 year. 



■»ii«in-< » »« fti »« w:i ii 



150 



1.0 



9 m 

® 9 



3C 273 



0.5 



« « « 



R 0.0 



9 9 



-0.5 






-1.0 
1.0 r- 



0.5 



R 0.0 



■0.5 



© a 



e « e 






9 a e 



» © 



-1.0 



-2.0 



-1.0 



0.0 



1.0 



2.0 



At (years! 



Figure 70. 3C 273. Optical and radio observations. The optical record consists of 100- 
day averages of photoelectric B magnitudes (Kunkel 1967) from 1962.0 to 1967.2, and 
Burkhead (1968, 1969, 1970, 1971, 1972, 1975) photoelectric B magnitudes from 1968.1 to 
1975.3. Royal Greenwich photographic B magnitudes (offset by -0?17) generally allign 
with these data, but have not been included. The radio record consists of 1.9-cm data 
from 1964.0 to 1966.3 (Allen e_t al. 1968); Algonquin 2.8-cm data (offset -3.0 Jy) from 
1966.5 to 1969.5; and Dent 1.9-cm data from 1969.5 to 1975.5. The dashed vertical lines 
indicate the transitions between the data sets. 



I2.6r- 

u 

§12.8 

gl3.0 

< 

^13.2 



OPTiCAL 






'.V 



? t 



« » 



* *, 



RADIO 



60.0 



r'l II 



l(!il,il!|i^ 



fi^i 



ihii 



! ) 



:.'.' 



"('Ill'',;' '-S,, < 






40.0 



>- 

•-3 



20.0 



1962.0 



I I I II I I I 1 — L__ 

64.0 66.0 68.0 



-L__-J_ 



JL. J 1 J L 



DATE 



70.0 



72.0 



±__J___l L_ 



74.0 



76.0 



U1 
K3 



153 



as illustrated by the R vs At plots in Figures 71 and 72. Inclusion 
of the initial steep radio rise recorded at 1.9 cm obviously invalidates 
the correlation, as can be seen in Figure 73. The maximum that then 
appears for the radio leading the optical by about 4.7 years is caused 
by an approximate alignment of the cyclic trends in the optical and the 
radio curves. It should be noted that the plotted optical data, prior 

to 1958.0, represent 100-day averages. These averages maintain a cyclic 

m 
character, with a maximum amplitude variation of ±0.4 from an average 

m 
magnitude of 12.75, that has been traced back to 1887 (Kunkel 1957). 

Thus there is no optical counterpart to the catastrophic radio outburst 
between 1964 and 1966.5, and any correlations which arise must be attri- 
buted to the approximately cyclic nature of both records unless and 
until there is a unique correlated event in both the radio and the 
optical observations. 

PKS 13544-19 
As might be anticipated from the nearly featureless optical record 
in Figure 74, there is no apparent optical-radio correlation, and the 
linear correlation procedures produce no results of interest, as can be 
seen in Figure 75. The only significant radio feature is a raonotonic 
rise beginning about 1971.0, which aligns with a gradual rise in the 
optical level between 1969.0 and 1972.0 to cause the broad maximum in 
the R vs At plots. One might make a weak argument that this is a 
correlation, but at most it is a one-event correlation. 



1.0 

0.5 

R 0.0 

-0.5- 

-1.0- 
1.0 

0.5 

R 0.0 

-0.5 
-1.0 



1 1 

to 
• 9 


3C 273 
•• 

• 


• • 

*• 

» • • 


• • ••• •• 

• • • 


••• ' 






*. *. . ...... 




... ^ • 

*. 


1 1 


• 

1 III 1 , .. 



-6.0 






• ^ • 



-4.0 



-2.0 



0.0 
Atlyearsl 



2.0 



4.0 



-6.0 



Figure 71. 3C 273. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for all the optical data but 
only the Algonquin 2.8-cm data, using actual data (top) 
and interpolated data (bottom), with At = At =0.0833 year. 






1.0 

0.5 

R 0.0 

-0.5 

-1.0 
1.0[ 

0.5 

R 0.0 



-0.5 
-1.0 



• • •« 



-6.0 



.• •••• 



-4.0 



-2.0 



• . ••• 



0.0 
At (years! 



3C273 



• M »« 



2.0 



4.0 



6.0 



Figure 72. 3C 273. Normalized cross-correlation coefficient (R) vs 
time shift (^t) for all the optical data but only the Algonquin 2 . 8-cra 
and the Dent 1.9~cra data, using actual data (top) and interpolated 
data (bottom), with At = At = 0.0833 year. 






Figure 73. 3C 2 73. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for all the optical and radio 
data presented in Figure 70, using actual data (top) and 
interpolated data (bottom), with At = At = 0.0833 year. 



1.0 

0.5 

R 0.0 

-0.5 

-1.0 
1.0 

0.5 



3C 273 



« « o • 



• • • • • 



• --• 



R 0.0 
-0.5 






»»««•••«•••» 



1.0 



■4.0 



■2.0 



0.0 
t (years 



2.0 



4.0 







1 967.0 



68.0 



69.0 



70.0 



^'•° DATE ^2° 



73.0 



74.0 



75.0 



76.0 



Figure 74. PKS 1354+19. Optical and Algonquin 2.8-cm observations. 
The optical record consists of Yale Observatory B magnitudes from 
1969.1 to 1971.0, and Rosemary Hill B magnitudes from 1971.2 to 1975.5. 



00 



Figure 75. PKS 1354+19, Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for the optical and radio data 
presented in Figure 74, using actual data (top) and interpolated 
data (bottom), with At = At^ = 0.1667 year. 



160 



1.0 



0.5 



R 0.0 






9 e 



1354 + 19 



« « 



• • 






-O.b 



-1.0 
1.0 



0.5 



R 0.0 



-0.5 



-1.0 





« 
• « » 

« 

« 
— • « 

» » 
e 

• 
• 


• • 

• 
* • 

e « 

— » — 

! 1 i 1 1 ■ 



-4.0 -2.0 



0.0 

At (years) 



2.0 4.0 



161 



OQ 208 
While the optical data in Figure 76 show obvious flare activity, 
the lack of conspicious features in the radio data precludes the 
establishment of a correlation, which is borne out by the scatter-diagram 
appearance of the top of Figure 77. The most convincing radio trend is 
a gradual rise beginning about 1970.0; there is no evidence of this in 
the optical record, which is admittedly sparse. 

PKS 1510-08 
Figure 78 reveals abundant radio activity and significant optical 
activity. However, in view of the short time-scale of the individual 
radio events (typically about six months), correlation with the somewhat 
sparse optical record is difficult. This conclusion is supported by the 
R vs At plot in Figure 79, the top half of Xirhlch resembles a scatter 
diagram, which is most likely due to the relatively sparse optical data. 
From 1967.0 to roughly 1973.0, the radio events appear to be super- 
imposed on a long-term decline for which there is no evidence in the 
optical data. 

NP.AO 512 
Visual inspection of Figure 80 suggests that the radio data follov; 
the optical data from the beginning of the optical record around 1970.4 
to 1972.9. However, after 1972.9 the apparent correspondence deterio- 
rates somewhat for the remaining short run of radio observations. This 
result is borne out by the correlation coefficients, which reach a 
maxim\im value of about 0.66 at roughly zero time delay for the total 




Figure 76. OQ 208. Rosemary Hill photographic 
magnitudes and Algonquin 2.8-cm observations. 



as 



0.5 



R 0.0 



163 



OQ 208 



9 • 



-0.5 



• • S 9 



-1.0 
1.0,- 



d 



0.5 



R 0.0 



• s 



-0.5 



4 o « « e * 

9 « 






-1.0 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 77. 00 208. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for the optical and radio data 
presented in Figure 76, using actual data (top) and inter- 
polated data (bottom), with At^ = At^ = 0.125 year. 



6.0 



lij 
o 

h- 



17.0 



18.0 



OPTICAL 



II ^ 



, RADIO 



* I.H( 



,ti*l 






, , .,, , M/V'i' . 



I 



I 

4 



i 



".' 



i 



li 



J L 






J L 



5.0 



3.0^ 



.0 



1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 76.0 



Figure 78. PKS 1510-08. Rosemary Hill photographic 
magnitudes and Algonquin 2.8-cm observations. 



.0 




-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 79. PKS 1510-08. Normalized cross-correlation coeffi- 
cient (R) vs time shift ( t) for the optical and radio data 
presented in Figure 78, using actual data (top) and inter- 
polated data (bottom), with t^ = t^ = 0.1 year. 



Ul 



Figure 80. NRAO 512. Rosemary Hill photographic 
] magnitudes and Algonquin 2.8-cin observations. 

J 

t 
! 



6.0 



r 



uj 1 7.0 

Q 

t 
(3 

:ei8.o 



19.0 



optical 



RADIO 



|lMtlt 



1968.0 69.0 




<» 



y 



ifl 1 1 



1 



ft 



III 



/"ill, ,iiii'"i'rif^ii^ 



t 



X-___J. — i—^ L_ — J — -J- 



J L 



ll 



70.0 71.0 72.0 

DATE 



A _1 



73.0 



74.0 



75.0 



3.0 



2.0^ 



.0 



76.0 






optical and radio data records, as shown in Figure 81. However, when 
1 optical data only through the end of 1972 are considered, the maximum 

' value of R jumps to 0,8 ± 0.1 for the radio record leading the optical 

I by 0.03 ± 0.3 year as shown in Figure 82. 

While a clearly defined maximum in the population of calculated 
correlation coefficients supports the correlation found by visual 
inspection of the data, caution must be exercised in the consideration 
of correlations between two sets of data which show activity on a 
similar time scale. It is this character of the data records which 
gives rise to a maximum value of R - 0.60 at At = +A.6 years in Figure 
81, when the 1968.4 to 1970.2 radio record aligns with a similar optical 
trend from 1972.6 to 1974.4. Similarly, the same radio feature aligns 
with the optical data from about 1970.4 to 1971.5 to give a maximum 
R = 0.7 at At - +2,0 in Figure 82 when only part of the optical data 
are used. 



3C 371 



Examination of Figure 83 suggests a possible correspondence 
between the prominent 1969.5 to 19 70.5 optical increase and the 1971 to 
1972 radio increase. These events are separated by At - -1.5 years. 
There is also some resemblance in the plateau regions following the 
increases. Unfortunately these impressions are not supported by the 
analytical study. The population of cross-correlation coefficients in 
Figure 84 basically wanders, although it does show a clearly defined, 
albeit relatively small, correlation coefficient of 0.55 for the radio 
data leading the optical by 0.5 ± 0.8 year. This results when the 
1971-1972 radio rise is superim.posed across the optical data gap around 



Figure 81. NEAO 512. Normalized cross-correlation coefficient (R) vs time shift (At) 
for all the optical and radio data presented in Figure 80, using actual data (top) 
and interpolated data (bottom), v^ith At = At = 0.0667 year. 



1.0 



NRAO 512 



0.5- 

R 0.0 

-0.5 

-1.0 
1.0 



0.3t 



R 0.0 



« a 



■0.5 
■1.0 



■4.0 



a c 



■2.0 



0.0 
At (years! 



2.0 



4.0 



o 



Figure 82. NRAO 512. Normalized cross-correlation coefficient (R) vs time shift (At) for 
all the radio data but only the optical data through 1972.8, using actual data (top) and 
interpolated data (bottom), with At^ = At^ = 0.0667 year. 



l.Or 
0.5- 

R 0.0- 

-0.5- 

-1,0- 
1.0- 

0.5 

R 0.0 

-0.5 

-1.0 



• a 



• • • 



m • 
■ « 



• • 



-4.0 



-2.0 



0.0 

Atlyearsl 



NRAO 512 



« • 



2.0 



0.4 






Figure 83. 3C 371. Optical and Algonquin 2.8-cm observations. The optical record 
consists of Royal Greenwich B magnitudes (offset -0"'25) from 1966.6 to 1969.6, and 
Rosemary Hill photographic magnitudes from 1969.0 to 19 75,8. 



14.0 



ijj 

Q 

3 



tl5.0 






OPTICAL 



16.0 



- 



RADIO 



J L 






f 







I i i 






■\ 


i 




i 1 



I i I I L_ L 



"II 



.'I' 



I 



ill 



w 



l'l,li"l'l'll/l'.\*l' ' ''•'' 



l' i*''"l|ll||H||,HtHl||,ii 



1966.0 67.0 68.0 69.0 70.0 



71.0 72.0 

DATE 



J I- 



-i_ L_ J- 



3.0 



2.0 >; 



73.0 74.0 75.0 76.0 



1.0 



4^- 



175 




15- 



R 0.0 



15- 



-II 



* * » 

o • 

, a* « • 

• . • .' 

• • • • . 


• 
• 

1 1 1 1 ! i 1 



-61 



-4.[ 



-2.0 



2.0 



4.[ 



6.0 



At (years) 



Figure 84. 3C 371. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for the optical and radio data 
presented in Figure 83, using actual data (top) and inter- 
polated data (bottom), with At = At = 0.1667 year. 



176 



1972,25. Because the more extensive optical variability contrasts with 
the relative radio inactivity on either side of the radio rise, this can 
probably be considered a one-event correlation. It will of course be of 
interest to see if the particularly well-defined optical flare in mid- 
1975 is reflected in future radio data. 

3C 446 

As another test of the correlation procedures, the total 1.9- and 
2.8-cin data records shovm in Figure 85 were correlated, resulting in the 
RvsAt plots illustrated in Figure 86, which show a maximum value of 
R = 0.92 for At = -0.3 and -0,25 years for the hole and the interpola- 
tion techniques respectively. 

Although the long-term radio and optical data records in Figure 87 
generally follow the same trends, the very violent optical flare at 
approximately 1974,7 has no obvious radio counterpart to date and is 
thus probably responsible for the absence of a significant analytical 
cross-correlation in Figure 88. However, it might be argued that the 
radio rise beginning near 1974.7 is the event that corresponds to the 
optical flare. If this were the case, both the value of At and the 
relative amplitudes would seem to be quite different for the 1970 - 1971 
and the 1974 - 1975 events, which makes the fit rather _ad hoc . 

PKS 2345-16 
Visual examination of the optical and radio records in Figure 89 
seems to indicate trends that follow one another rather well for At 
= -0.9 year. However, the family of calculated cross-correlation 
coefficients shown in Figure 90 simply oscillates as a function of At, 



6.0 



4.0 



2.0 



if f 






M* 



^^ .; 






3C 446 






f i^ 



^^ 






t't*,. 






A 



6.0 



4.0 



>- 



1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 76.0 

DATE 



2.0 



Figure 85. 3C 446. Dent 1.9-cm observations (top) 
and Algonquin 2.8-cm observations (bottom). 






Figure 86. 3C 446. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for the two radio records in 
Figure 85, using actual data (top) and interpolated data 
(bottom), with At = At„ = 0.125 year. 



iiiae»;» -e5»»jp"&'*« — 



179 



.5 - 



R 0.0 



].5 



1 . «* I 1 

3C 446 

« S 

• 
• 

9 

• 

• 


« 

• 

« 
i 



I.Or- 



0.5- 



R 0.0 



-1. 



• 
« « 

9 

• 
• 

• 

• 

• 

• 





.5 - 



-2.0 -1. 



1.0 2.0 



A t (years! 



Figure 87. 3C 446. Rosemary Hill optical magnitudes and Algonquin 2 . 8~cm 
observations. The optical record consists of photographic magnitudes corrected 
to B magnitudes from 1969.0 to 1970.8 and B magnitudes thereafter. 



o 

CO 



o 

to 



o 



o 

cri 



o 



O 



O 



O 



UJ 

I- 
< 



N 



O 

d 



O 
CJi 



< 
O 

Q. 

o 



o 

< 



o 

CD 



O 
CD 



o 


o 


O 


O 


o 


lO 


U3 




CO 


cr> 



182 



1.0 
0.5 



'■»»• •— 



3C 446 



R 0.0 



-0.5 



a • 



-1.0 -_ 
inn, 



0.5 



R 0.0 



-0.5- 



-4.0 



-2.0 



0.0 
At (years) 



2.0 



4.0 



Figure 88. 3C 446. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for the optical and radio data 
presented in Figure 87, using actual data (top) and inter- 
polated data (bottom), with At = At^ = 0.125 year. 



183 




O 
CD 



O 

LO 



o 



N 


u 

•H 




r^ 








pu 




n) 




M 




M 




• 


o 


4-1 Oj 

c 


ro 


^ O 


N 






l-i cfl 




rH > 




•H iJ 




rn n 




m 




;^ .Q 


o 


u o 


c\i 


e e 


r- 


OJ a 
« 1 




o CO 


UJ 


C-; . 


t- 


CM 


< 


• c 


Q 


O -H 




.H a 


o 


1 cr 




1/1 c 




<r O 


N 


n M 




CN rH 




< 




00 




W -o 




P4 c 




c3 


o 


• cfi 


o 


00 T3 


N 


— t 




Ci) u 




'H -H 




3 C 




M M 




•H Cti 




f=H e 


o 




CD 




(D 





o 

CO 
CD 
(7) 



3aniiN9vi^ 



Figure 90. PKS 2345-16. Normalized cross-correlation coeffi- 
cient (R) vs time shift (At) for the optical and radio data 
presented in Figure 89, using actual data (top) and inter- 
polated data (bottom), with At = At = 0.625 year. 



185 



0.5 



R 0.0 



-0.5 



-1.0 
1.0 




0.5 



R 0.0 



-0.5 



-1.0 



99 

« 

• 
e » » 

® « 
e ® • 


• 

« 

« ® 



-4.0 -2.0 



0.0 
At (years 



2.0 4.0 



186 



showing no single significant maximxim for either the hole or the inter- 
polation techniques. This behaviour doubtless results from the succes- 
sive superposition of the several small peaks in each record, and the 
analytical method thus fails to support any single value of At, The 
visual correlation is nevertheless attractive enough to suggest further 
study. 

Summary 

In an attempt to find any relationship that might exist between 
various types of variability and any real or potential correlations 
between radio and optical activity as determined by this study, Table 5 
lists all the sources studied in this work, together with their activity 
subclasses and a subjective evaluation of the strength of any correla- 
tion found in this investigation (a "No" of course means that no 
correlation was found) . The evaluations result from a weighing of both 
the formal analysis as summarized earlier in Table 4 and a visual exam.- 
ination of the data. The second column of the table designates the type 
of object as "Gal" (galaxy), "Lac" (BL Lacertae object), or "Q30" 
(apparently normal quasar) . 

The activity subclasses, which have been defined previously by Dent 
_et al. (1974) and more specifically by McGimsey _et _al . (1975), include 
the following. Subclass I consists of objects whose light or radio 
curves are dominated by rapid, short-term "flickering". Long-term 
trends are inconspicious and very gradual if present. BL Lac is a 
classic example. Subclass II is characterized by prominent, long-term 
variations in mean level, with minor excursions or flickering about the 
changing mean, as in OJ 287. Subclass III exhibits a mixture of short- 



TABLE 5 

Sron-IARY OF CORRELATION ANALYSIS RELATIVE TO OPTICAL 
AND RADIO VARIABILITY SL^CLASSES 



187 





Type of 


Optical 


Radio 


Evaluation of 


Source 


Obiect 


Subclass 


Subclass 


Correlation 


OJ 287 


Lac 


II 


II 


Strong 


3C 454,3 


QSO 


I 


II 


Fair 


BL Lac 


Lac 


I 


I 


Marginal 


CTA 25 


QSO 


II 


III 


Marginal 


PKS 0405-12 


QSO 


V 


V 


No 


PKS 0420-01 


QSO 


IV 


II 


No 


3C 120 


Gal 


III 


III 


No 


NRAO 190 


QSO 


III 


II 


No 


PKS 0458-02 


QSO 


V 


III 


No 


3C 138 


QSO 


II 


V 


No 


PKS 0735+17 


Lac 


III 


II 


Marginal 


PKS 0736+01 


QSO 


III 


II 


No 


01 363 


QSO 


V 


V 


No 


OK 290 


QSO 


III 


II 


No 


3C 273 


QSO 


II 


II 


No 


PKS 1354+19 


QSO 


II 


II 


No 


OQ 208 


Gal 


II 


III 


No 


PKS 1510-08 


QSO 


III 


III 


No 


NRAO 512 


QSO 


III 


II 


Fair 


3C 371 


Gal 


III 


II 


Marginal 


3C 446 


QSO 


III 


II 


Marginal 


PKS 2345-16 


QSO 


IV 


II 


Marginal 



188 



and long-term effects of comparable amplitudes with neither effect 
dominating, as in the light curves of 3C 120, 3C 371, and NRAO 512. 
Subclass IV is "episodic", consisting of objects which display long 
periods of relative quiescence, punctuated by shorter intervals of 
violent activity, as in the light curves of PKS 0420-01 and PKS 2345-16, 
Finally, Subclass V has been added for those objects which show little 
activity at all, such as 01 363. 

The most striking observation from. Table 5 is that of the nine 
sources for which some degree of correlation was suspected, seven show 
radio variation of a character that places them in activity Subclass II, 
a group that displays relatively smooth, long-term changes in level. It 
might, in fact, have been suspected in advance that this group would be 
the easiest in which to find long-term correlations. The optical 
variations of the nine sources are more uniformly distributed between 
the subclasses, with two being assigned to each of Subclasses I and II, 
and four to Subclass III; one of the optical variables was character- 
ed as Subclass IV. 

The foregoing comments emphasize a significant observation that can 
be made based on the figures illustrating the combined radio and optical 
activities as functions of time. The radio and optical variations of a 
given source may display quite different characteristics. CTA 26, 
PKS 0458-02, PKS 1354+19, and 3C 273 (at least recently) are clearly 
more active in the radio region than in the optical. Conversely, 3C 138, 
Oq 208, PKS 0420-01, and PKS 2345-16 seem to display relatively more 
activity in the optical spectrum than in the radio. In the cases of 
3C 454.3, NRAO 190, PKS 0735+17, and 3C 446 the records suggest that 
optical activity occurs on a shorter time scale than the radio events. 



189 



Of the three galaxies in the table, only 3C 371 showed marginal 
evidence of correlation. About the same ratio of "normal" QSO's, five 
out of sixteen, can be described as displaying some evidence of 
correlation. 

It is interesting that all three of the objects identified in 
Table 5 as Lacertids were also identified as displaying at least margin- 
al evidence of correlation between the optical and radio records; the 
one strong correlation, that of OJ 287, is of course for a Lacertid. 
While the characteristic violence and short time scale of these objects 
is conducive to correlation studies, caution must be exercised because 
the relatively frequent occurence of roughly equal-time-scale activity 
in both the radio and the optical can lead quite easily to spurious 
correlations. 

It should be emphasized that the linear correlation of optical 
mangitudes with radio flux that is presented here is intended only as a 
first attempt to search analytically for correlations, and negative 
results are not necessarily final. In general great care must be 
exercised in drawing conclusions from unevenly spaced time series which 
often involve relatively sparse sam.pling and often result in one-event 
correlations. While such correlations may in fact be real, not infre- 
quently an examination of the entire data racord casts doubt on the 
validity of such correlations; and in general until further data in- 
dicate otherwise, the conservative approach is to regard these one-event 
correlations as coincidences between random processes. 

The closeness of the fit between the optical and radio records for 
OJ 287 for a period of about five years leads to the conclusion that 
this is indeed a real correlation. In addition, sufficient evidence 



190 



exists for possible correlations in several other sources to warrant 
more concerted obser-^ing efforts at both optical and radio wavelengths. 

In those cases where no significant visual or analytical cross- 
correlation was found, it is still premature to conclude that the 
optical and radio events are totally uncorrelated. There are at least 
five possible explanations for such negative results. 

a) Gaps in coverage have caused optical and/or radio events to go 
unobserved, (In most cases it is the optical record that is least 
complete. ) 

b) The activity may be correlated, but with a time lag so great 
that data have not been collected over a long enough period of time 
to establish the correlation. In view of the lengths of some of 
the records presented here, this becomes increasingly unlikely, 

c) The activity may be correlated, but with a different functional 
relationship between optical and radio emission than has been 
tested analytically here. (This should not, however, preclude the 
observation of visual correlations.) 

d) For a given source, some events may be correlated while other 
events appear in only one of the two spectral regions. Similarly, 
the time lag At might vary from event to event. In either of these 
cases, the search for a correlation becomes very challenging indeed. 

e) No real correlation exists between optical activity and radio 
activity. 



CHAPTER V 
CONCLUSIONS 



Spectral Energy Distributions 
In considering the theory and results of this study, two points 
regarding the spectral energy distribution of extragalactic variables 
need a cautionary clarification. Because this study concerns itself with 
sources that exhibit both optical and radio emission, the spectral energy 
distributions of the sources considered are generally of the form sunma- 
rized by most of the distributions in Figure 91; that is, they exhibit a 
relatively low optical flux that rises into the radio spectral region. 
However, this is not true for all extragalactic sources; many sources do 
not show a rise into the radio frequencies and thus are either radio quiet 
or exhibit a radio flux of amplitude comparable to the optical flux. 

Also with respect to the spectral energy distributions, some confu- 
sion may exist regarding extrapolation of the predictions of the simple 
expanding source model to optical wavelengths. Figure 92 is an idealized 
portrayal of the spectrum of an extragalactic variable at a given time t. 
Curve 1 represents the contribution to the spectral energy distribution 
from an optically thin, adiabatically expanding cloud of relativistic 
electrons that has resulted from a flare event that began at some previous 
time. Curve 2 represents the contribution to the spectral energy distri- 
bution from another cloud of relativistic electrons that has resulted 
from a flare that can be observed at this time at frequencies higher than 
y, . This second cloud is optically thick from v to the frequency v , 

191 



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195 



where it becomes optically thin. For frequencies greater than v , curve 

m 

2a represents the case where the slope and thus the spectral index (a) of 
curve 2 is greater than the spectral index of curve 1; curve 2b repre- 
sents the case where the two spectral indices are equal; and curve 2c 
represents the case where the spectral index of curve 2 is less than that 
of curve 1. Solid curves A, B, and C represent the total spectral energy- 
distribution for the source, and thus reflect the superposition of the 
contributions from curves 1 and 2 for the three cases just reviewed. 

Assuming the spectrum results from synchrotron emission and using 
curve 1 as a reference flux level, as one observes at higher frequencies, 
at a given time t one expects to observe a higher peak flux (PF in Figure 
92) and a higher flare amplitude (FA) only as long as the source remains 

optically thick (v<v ). At the same time t, as one observes at frequen- 

m ^ 

cies v>v the peak flux will decrease, vrhile the flare amplitude xjill be 
a function of the spectral indices of curves 1 and 2; that is, the flare 
amplitude will be greater at higher frequencies if conditions support 
curves 2a and A, but the flare amplitude will be less if conditions sup- 
port curves 2c and C. 

The simple expanding source model assumes an instantaneous production 
of particles, resulting in a source which is initially optically thick at 
inf initesmally small wavelengths. In a real source, however, (Kellermann 
1972) the production of particles must occur over a finite period of time 

and throughout a finite volume of space. Thus above a frequency v the 

" -^ m 

source must be always optically/ thin, and the observed intensity varia- 
tions will reflect the rate of acceleration of relativistic electrons as 
well as changes in magnetic field strength and electron energy distribu- 
tion. For V > V , there is no expected delay in the time when the peak 



196 

amplitude is reached at different wavelengths, and the maximuin flux density 
reached is less than that predicted by the simple model on the basis of 
extrapolating an optically thick spectral energy distribution to higher 

frequencies. Some data at millimeter wavelengths suggest that v ^ 30 GKz 

ffl 

(X = 1cm), The extensive Algonquin Observatory data at 2.8 and 4.5 cm 
indicate a number of sources for which v ^ 6 GHz (A = 4.5cm). Finally 
it should be recalled that the slope of the spectral energy distribution 
for an optically thin source will be a function of the electron energy 
distribution only, Thus in Figure 92 the flare amplitude at v may be less 
than, equal to, or greater than the flare amplitude at v This is con- 
sistent with the results noted in Chapter II, that QSO's sometimes get 
redder and sometimes bluer during outbursts. Within the limitations 
imposed by our general ignorance of the infrared spectral energy distri- 
bution, and the possible curvature of the optical spectral energy distri- 
bution which may im.ply a non-synchrotron component of the radiation, one 
can come to the following tentative conclusion. If one assumes that the 
entire spectrum is caused by synchrotron ratiation, then it seems reason- 
able to conclude from the previous discussion that the optical emission 
originates from an optically thin source. This is supported by Figures 1 
and 91, which indicate that in general there is a long decrease in flux 
level between radio and optical wavelengths. While changes in the flux 
level of an .order of magnitude or less are observed at radio frequencies 
(Kellermcinn and Pauliny-Toth 196S) and at optical frequencies (Figures 
11 and 12) , there appears to be no evidence of a change in the overall 
character of the spectral energy distributions, in which the radio flux 
is often two to three orders of mangitude higher than the optical flux. 



197 



Lack of Correlation 
After reviewing the results of the correlation analyses presented in 
Chapter IV, one must separate conclusions into at least two categories. 
What can be determined from the apparent lack of conclusive correlation 
between optical and radio activity found for most sources with the obser- 
vations to date; and what can be concluded from the strong correlation 
found in the cases of OJ 287 and 3C 454.3? Finally, one must address 
the question of what further investigations can be made either to test, 
strengthen, or supplement the results presented herein. 

The lack of demonstrable correlation for most sources analyzed in 
this work permits txro important conclusions to be drawn. First, the fact 
that certain sources have a quite active radio spectrum but a quiescent 
optical spectrum, or vice-versa, suggests that in those sources the radio 
and optical emissions may be independent of each other. This may be due 
either to a physical separation of the regions which emit optical and 
radio radiation and the accompanying lack of a coupling mechanism, or to 
the fact that the flare itself may have a limited spectral distribution. 
Thus the radiation source is stable at some frequencies while it is un- 
stable at others. In addition, the apparently uncorrelated optical and 
radio activity in other sources is consistent with a Christmas-tree type 
of model in which localized regions within the source as a whole emit 
sporadic outbursts with quite different spectral distributions, probably 
as the result of disparate local conditions. Note that if this model is 
valid, coupling mechanisms may exist between localized regions which 
would imply relationships between activity observed from different 
localized regions, although the activity could not be correlated if 
localized conditions were of a sufficiently varied character. Thus in 



198 



all these cases of non-correlation, the evidence indicates that extrap- 
olation of the simple expanding source model from radio to optical wave- 
lengths is simply not meaningful. 

Secondly, the lack of radio-optical correlation has a significant 
impact on the problem of quasar energetics; for if no relationship exists 
between the radio and optical spectra, the energy associated with any 
single event is significantly reduced. This is best illustrated by an 
example, using the expression (Burbidge and Burbidge 1967) 

2 2 



Aire 
■v Ho ^v 



F , - —r. — f . 2~ (ergs/sec/Hz) 



(1 + z") 

for a cosmology with a deceleration parameter, Or, = + 1, where F is the 
total radiated energy per unit time per unit frequency interval, f is 
the observed flux per unit frequency interval at the observational fre- 
quency. Ho is the Hubble constant, c is the velocity of light, and z is 
the redshift of the spectral lines. If Ho = 50 km/sec/Mpc and z = 1, 
then assuming an idealized step-function flare lasting three months, a 

radio flare having an amplitude of 20 Jy (20 x 10~^^ watts/m~/Hz) between 

9 -2 ""2 

10 cm (3 X 10 Hz) and 10 cm (3 x 10"" Hz ) or an optical flare from 

13.5 to 12?5 (10 Jy) betV7een 100 nm (3 x lO"'"^ Hz) and 1000 nm 

(3 x 10 Hz) will emit a total energy on the order of 10 ergs. It is 

obvious that if such a flare is observed only in the radio or only in 

the optical spectral region, the source mechanism of the flare will emit 

much less energy than if a single event is required to radiate in not 

only the radio and optical spectral regions, but also in the intervening 

frequencies. 



199 



OJ 287, BL Lac, and 3C 454.3 
Before discussing the implications of a radio-optical correlation, 
it is important to review some opinions and important facts regarding 
sources of particular interest. BL Lac is included although it shows no 
strong correlation, because it is a source of great interest. 

There exists important opinion that, assuming there are no infrared 
or other excursions from the smooth spectra of OJ 287 and BL Lac in 
Figure 91, the entire continuum spectral energy distribution may be due 
to synchrotron radiation (Visvanathan 1973b and Stein 1975), In the 
case of OJ 287 this is supported by the lack of color change in the 
infrared or L^V observed by Smith et al. (1975) and by Rieke and Kinman 
(1974). In addition, the general shape of the energy distribution, the 
amplitude variability, the high variable polarization, and the apparent 
correlation between infrared and optical activity, as illustrated for 
OJ 287 in Figure 93, lead to the idea that the infrared and optical ra- 
diations originate in the same volume of space (Rieke and Kinman 1974). 

However, Kinm.an (1975) feels that the fact that the OJ 287 spectrum 
becomes flatter towards the infrared may indicate that the source becomes 
optically thick at 20 to 30 p. This lends support to his next specula- 
tion, that although the radio and optical radiations have a common 
particle s-apply, they probably are generated in different localized 
regions of the source. Finally, it is his opinion that the short-term 
radio variations are difficult to explain by the simple expanding source 
model. 

At least a rough approximation of the overall characteristics of the 
spectral energy distribution for OJ 287, BL Lac, and 3C 454.3 is given 
by Figure 91. This figure indicates that for all three sources, there 



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202 

is apparentl]/ a long decline in flux density with increaseing frequency 
all the way into the optical spectrum. VJhile optical and radio spectral 
distributions are known to change with time, the changes are not more 
than an order of magnitude change in fltix; thus the basic shape or 
character has been preserved over the time these objects have been 
observed. 

If we assume all the emission is s^mchrotron, then because we have 
not observed a flux level in the optical spectrum that could be obtained 
by extrapolating from the radio flux level, we can conclude that to with- 
in the accuracy of the present data the radio flux at frequencies less 
than the turnover frequency, v , is emitted from an optically thick 
region while the radio flux at higher frequencies and the optical flux 
are emitted from an optically thin region. Thus the optical emission 
from any correlated activity would appear to originate from either a 
thick or thin source depending on the turnover frequency, which may 
change with time. If the radio em.ission originates from the same opti- 
cally thin source as the optical, there should be no time delay, while 
if it originates from an optically thick source, a time delay will exist. 
A visual examination of the sparse data for OJ 287 in Figure 93 indicates 
a possible time delay from the optical, through the infrared, into the 
high-frequency radio. This is reinforced by the results of the present 
correlation analysis for all the available data as summarized in Table 4; 
however, the analysis of the data subsequent to 1972.75 indicates no 
time delay, Tvith a rather large error estimate. 

Of course an important alternative that should not be ignored is 
that the emitted radiation is not all synchrotron. 



203 



Table 6 lists the radio and optical amplitudes for the OJ 287 flare 
centered at about 1973.1. Column one lists the maximum and minimum flux 
levels in optical B magnitudes; column two' lists the maximum and minimum 
flujc levels in fl^sK. units; column three shows the change in stellar mag- 
nitudes; and column four lists the linear factor by which the flux 
levels changed. For a complete presentation of the relative optical- 
radio flux levels, optical B magnitudes were converted to flux units and 
radio flux values were converted to a magnitude scale using equation 
(31) from Chapter II 

m = -2.5 log F - C 

where m is the magnitude, F is the corresponding energy flux in units of 
10" Janskys, and C is a constant equal to 56.04. Table 7 lists the 
radio and optical amplitudes for the BL Lac flare centered al 1973.5; 
and Table 8 list the amplitudes for the 3C 454.3 radio flare centered at 
1972.5 and the optical flare centered at 1971.0. 



TABLE 6 

RADIO AND OPTICAL AMPLITUDES FOR 
OJ 287 FLARE 



Optical Blue 
Magnitude 



Flux 



Change in 
Stellar 



-96 2 
(10 ~ W/m /Hz) Magnitude 



Change by 
Factor of 



Optical Maximum 13.6 
Optical Minimum 16.0 



1.4 X 10 

1.5 X 10 



-2 
-3 



2.4 



9.1 



Radio Maximum 
Radio Minimum 



6.57 
7.66 



9.0 
3.3 



1.1 



.. / 



204 



TABLE 7 

RADIO AND OPTICAL Ai'EPLITUDES FOR 
BL LAC FLARE 



Optical Blue 
Mamitude 



Flux 



Change in 
Stellar 



— 9 A 9 

(10 VJ/m /Hz) Magnitude 



Change by- 
Factor of 



Optical Maximum 


15.0 


3.8 X 10 


Optical Minimum 


16.5 


9.6 X 10' 


Radio Maximum 


6.36 


11.0 


Radio Minimum 


6.77 


7.5 



-3 



1.5 



0.41 



4.0 



1.5 



TABLE 8 

RADIO AND OPTICAL AMPLITLT)ES FOR 
3C 454.3 FLARE 



Optical Blue 
Magnitude 



Flux 



Change in 
Stellar 



(10 ^ W/m /Hz) Magnitude 



Change by 
Factor of 



Optical Maximum 


16.3 


1.1 X 10 


Optical Minimum 


16.9 


6.7 X 10 


Radio Maximum 


6.06 


14.5 


Radio Minimum 


6.46 


10.0 



-3 



0.6 



0.4 



1.74 



1.45 



Implications of Correlation 
Unfortunately, no obvious conclusions can be drawn from a strong 
ratio-optical correlation, because there are still too many unknown 
parameters. IvTiile in-depth theoretical investigation of the implications 
of the data presented lies beyond the scope of the present work, such an 
investigation could eliminate some of the alternatives and thus lead to 
a valid conclusion. The primary purpose here will be to review and 
briefly discuss potential explanations for the correlated activity. 



205 



A long-term correlation may be a function of either the source or 
the intervening medium. If it is a function of the source and if we 
assume the entire spectral distribution is caused by s3mchrotron radia- 
tion, then the spectra in Figure 91 suggest that at the time they were 
measured, the 2.8-cm (1.07 x lO"" Hz) radiation was emitted from an 
opaque region of OJ 287 and a transparent region in 3C 454. 3, although 
in both cases the data are inadequate to determine completely the fre- 
quency at which the source becomes optically thin. In the case of OJ 287, 
one might argue that prior to 1972.5 the source was optically thick, 
while after 1972.75 the source became transparent at 2.8 cm, thus causing 
the correlation analysis to indicate a time delay before 1972.75 but no 
time delay thereafter. However, the spectral energy distribution indi- 
cates the source is obviously transparent from optical to Infrared wave- 
lengths, while the curves in Figure 93 suggest a possible time delay. 
In the case of 3C 454.3, the spectrum in Figure 91 appears to be in 
conflict with the time delay found between possibly correlated optical 
and radio activity in this study. Finally, note that all these tentative 
statements are based on the assumption of a smooth spectral distribution 
through the infrared wavelengths, for which there is little if any data. 

If 3C 454.3 were opaque between 20 and 300 y, this could explain 
the relatively long time delay between optical and radio activity. Also, 
one could start considering changing opacities as the cause of varying 
time delays, but this is extremely dangerous because the similarities 
between radio and optical activity invite spurious correlations. 

If the intervening medium is the cause of variations, the medium 
could be either gas or dust or a mixture of the two. In general, optical 
radiation will be absorbed and scattered by dust, while radio, radiation 



206 

will pass through the dust because radio wavelengths are much greater 
than the dimensions of dust particles. Thus if an intervening dust 
cloud caused caused variations of a source, the effect would be observed 
in the optical, but not the radio wavelengths. 

If the intervening medium were a gas cloud of reasonable density, 
the gas xTOuld selectively absorb only certain spectral lines, allowing 
m.ost of the optical radiation to pass through. If the gas were close 
enough to the source, it would selectively emit at only definite spectral 
line frequencies. Lyuty and Pronik (1975) have in fact observed varia- 
tions in the intensity of Ha lines in Seyfert galaxies which copy contin- 
uum changes after a delay of 20 to 30 days. In addition, Williams and 
Weymann (1976) have reported finding a extragalactic gas cloud in front 
of, but not associated with, the quasar PHL 1222, by the detection of 
absorption lines in the optical spectrum. 

uJhile the correlation in OJ 287 is intriguing and compelling for 
further investigation, it must be remembered that this is the only case 
of conclusive correlation among the 22 sources studied here, and the 
hundreds of other sources for which there is insufficient data to search 
for a correlation. Thus one cannot draw the conclusion that the cause 
of the correlation in OJ 287 can be extended to other extragalactic 
variables. The similarity of OJ 287 to other EGV's may bias one towards 
acknowledging that the correlation must therefore result from something 
intervening rather than from the source itself. However, OJ 287 is 
sufficiently unique among EGV's that the correlation may well be a 
function of this particular source, and involve a mechanism not generally 
found am.ong extragalactic variables. In addition, the time scale of the 
long term bump in both the optical and the radio causes one to consider 



207 

whether a different kind of process is giving rise to the long-term 
activity in contrast to the short time-scale variations. 

Within the meager amount of hard evidence available, a Christmas- 
tree type of source would be consistent with the OJ 287 data, with 
multiple localized source regions having their own spectra and being 
stimulated by the same source mechanism through some kind of a coupling 
mechanism acting between the localized emission regions. Thus the over- 
all spectral energy distribution would be the superposition of many 
separate components. However this would require far different local- 
ized conditions to cause individual regions to emit only certain spectral 
energies. 

An accurate knowledge of the whole spectral energy distribution and 
its changes with time is a necessary prerequisite to understanding the 
nature of the continuum radiation mechanism. A theoretical understand- 
ing of the dynamics of these observed flares will probably require an 
amalgam of the theories of the simple expanding source, prolonged injec- 
tion of particles, and inverse Compton scattering and synchrotron energy 
losses (Stein 1975). 

Further Work 
To continue the search for answers to the many problems discussed 
in this work, there are many areas of investigation, both within the 
framework of the analysis described in this work and exterior to it, 
which should be followed up. 

1) The baseline should be removed from the OJ 287 radio and light 
curves to determine if a short-term correlation still remains. 

2) The optical and radio fluxes should be put on the same scale; 
then tests for both linear and non-linear functional correlations should 



208 



be carried out. This is probably best accomplished through both regres- 
sion and correlation analyses used iteratively. Correlation analysis 
will suggest an optimal time delay for a regression analysis, which will 
suggest the possible functional relationship between the variables, and 
this can in turn be compared with other functional relationships through 
correlation analysis. 

3) Angione (19 71) suggested a possible correlation between sparse 
optical and 9.5-iam data for 3C 454.3 between January, 1966 and May, 1968. 
During this period, the activity reflected in the 9.5-nnn data signifi- 
cantly differs from the Algonquin 2.8-cm data over much of the same 
period. The short wavelength radio activity and its relation to the 
optical data could probably be investigated further. 

4) VLSI observations using at least three baselines are desirable 
on a regular basis to determine the source structure, its changes with 
time, and the possibly localized source (s) of the radio radiation. This 
kind of regular \TLBI data is highly desirable both for OJ 287 and for 
other variable sources. 

5) Although difficult and time consuming, both optical and radio 
polarization observations would help to determine if the optical and 
radio radiations are emitted from the same region of a source, both for 
OJ 287 and other variables. 

6) While certainly difficult, better time resolution at optical 
wavelengths is highly desirable. 

7) The infrared spectrum must be investigated to determine if 
there is any structure in that portion of the spectral energy distri- 
bution for active sources. Such structure could be caused by emission 
from synchrotron electrons, Compton scattering, or dust. 



109 



8) While presently unrealistic, the most important observations 
that could be made would be to study the whole spectral energy distri- 
bution from centimeter-radio to X-ray wavelengths with high signal-to- 
noise ratios, to watch the evolution of the spectral distribution with 
time. 

Finally, the interpretations of this research are obviously biased 
towards a synchrotron, expanding source emission model for the reasons 
summarized in Chapters I and II, "Ivhile the meager conclusions I have 
drawn are scientifically consistent and reasonable, they are obviously 
colored by many assumptions. Other assumptions and interpretations may 
contradict what has been presented here, yet may prove to be valid and 
meaningful. 



APPSM)IX I 
COtrPUTER PROGRAMS USED IN THE STATISTICAL ANALYSIS 

Included in this appendix are listings of the programs C0REL2 and 
LrNREG2 and the accompanying subroutines that were used in the statis- 
tical analysis described in Chapters III and IV. 

To calculate cross-correlation coefficients, the program deck should 
be ordered in one of the following ways. For non- interpolation use: 

Program C0REL2 

Subroutines DATFUG (Version 1) 
PPLOT 
CORREL 

For interpolation use: 

Program C0REL2 

Subroutines DATFUG (Version 2) 
LININT 
SETUPl 
PPLOT 
CORREL 

Similarly, to generate a linear regression plot for the non-interpo- 
lation case use: 

Program LINREG2 

Subroutines DATFUG (Version 1) 
LINREG 



210 



211 



For interpolation use: 

Program LINREG2 

Subroutines DATFUG (Version 2) 
LININT 
SETUPl 
LINREG 

Linear regression plots were generated on the printer by executing 
calls to the subroutines PLOTl, PL0T2, PL0T3, PL0T4. These subroutines 
are part of the computing system at the Northeast Regional Data Center 
of the State University System of Florida, and their use is described in 
in documentation which is available to the user. PLOTl specifies the 
size of the plot and the separation between tic marks on the axes; PL0T2 
specifies the scales of the axes by submitting the maximum and minimum 
values of the axes; PLOTS plots LCNT points from the txTO specified 
arrays, assuming that the i-th value from array one corresponds to the 
i-th value from array two; PL0T4 labels the vertical axis, while the 
horizontal axis is labeled by a WvITE statement. At the time this 
analysis was conducted (November, 1975 to February, 1976), all that was 
required was that the subroutines be called in the proper order, with 
the correct arguments. 

The subroutine PPLOT was written by Dr. James Kennedy, who gener- 
ously gave me the code for my use. It includes the option of performing 
a Hanning smoothing on a data array by calling a subroutine SMOOTH. 
However, this smoothing subroutine was not used in the analysis and thus 
it is not included in this appendix. 

The programs C0REL2 and LINREG2 will accept data either from cards 
or from 80-column card images on disc. Data from a number of sources 
can be input at the same time provided that there is a blank card 



212 



separating each data record, that is betvreen the radio data and the 
optical data for the same source, and between the optical data and the 
radio data for different sources. The order of the data sets is not 
important to the actual execution of the programs; however, the conven- 
tion followed in this work was that for a given source the radio or 
lower frequency data preceded the optical or higher frequency data. This 
convention is important in the interpretation of the program output, 
because it determines whether the radio activity is lagging or leading 
the optical activity. 

At the beginning of each data record, both programs expect three 
header cards. The first header card contains the observatory identifi- 
cation and radio wavelength or frequency, if applicable, in columns 20 
to 34 and the source identification and optical frequency (U,B,V, or P) , 
if applicable, in columns 45 to 56. The next two cards are merely 
headings for columns of data. The programs read only the three fields 
which are listed under the column READ FORMAT in Table Ai from the 
data cards. 

One obvious update of the computer code listed in this appendix 
would be the creation of a single subroutine DA-TFUG xjhich can either set 
-99.0 flags to indicated holes for the non- interpolation case or inter- 
polate for the interpolation case. This was not done initially because 
of restrictions on running time and core size imposed by the priority 
under which the programs were executed. 



213 



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APPENDIX II 
FURTHER USE OF COMPUTER PROGRAi^IS AKD DATA BANK 



During the active phase of the statistical analysis, the data bank 
used for this study existed both on cards and in a partitioned data set 
which consisted of SO-column card images. Each entry in the data bank 
had the format listed in Table A-1. 

TABLE A-1 

DATA BANK FORMAT 

Column Contents Read Format 

1-10 Source Identification A4 

13-14 Beginning Month 

16-17 Beginning Day 

19-20 Beginning Year 

23-24 Ending Month 

26-27 Ending Day 

29-30 Ending Year 

33-43 Julian Date 

46 M for Mangitude or 
F for Flux 

48-52 Magnitude or Flux Value F5.2 

54 U, B, V, or P 

57-61 Error 

64-71 Middate of Observation F8.5 

78-80 Observatory Identification 

At the end of the active statistical analysis, this data bank 
together with all the programs used in the analysis were copied twice 
to the 9-track tape named OUASAPv. This tape is stored in the tape 



:35 



237 



library of the Northeast Regional Data Center of the State University 
System of Florida. 

In addition to that tape, the following material is kept in the 
Astronomy Department: 

1) a listing of the disc data set that was transferred to the tape 
QUASAR (this includes both data and programs); 

2) the listings from the creation of files 1 and 2 of QUASAR; 

3) a listing of a program (lEBUPDTE) that can be used to create a 
partitioned data set from the tape QUASAR; 

4) the card version of the data bank 

5) a summary of the materials kept in the department. 

To begin the kind of analysis summarized in this dissertation, two 
approaches may be taken: 

1) use the listing of the original disc data set as a guide to 
punch the desired material from the tape QUASAR; or 

2) use the listing of lEBUPDTE as a guide to recreate the parti- 
tioned data set from the tape QUASA-R; then punch the program PUNCHOOl 
from the listing of the original disc data set. This program can then 
be used to dump whatever code or data is desired from the disc data set. 

Finally note that one change has been made to the code found on the 
tape QUAS/vR. Tnis change is included in the program listings in 
Appendix I, and consists of a statement added to the subroutine CORREL 
between statements 130 and 40. Also note that the program documentation 
accompanying the listings in Appendix I has been updated relative to the 
documentation which appears on the archival tape QUASAR. 



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BIOGRAPHICAL SKETCH 

Richard Bryan Pomphrey was born on May 11, 1946, in St. Louis, 
Missouri,, He graduated from St. Louis University High School in May, 
1964, and began his undergraduate studies as a Chemistry major at Regis 
College in Denver, Colorado. He transferred to the School of Engineer- 
ing at Washington University in St. Louis, Missouri, from which he 
received a Bachelor of Science degree with a major in Physics in May, 
1969. In September, 1969, he entered the Graduate School of the 
University of Florida where he worked as a graduate assistant in the 
Department of Physics and Astronomy until June, 1973. During that 
period, he completed the course work leading to the degree of Doctor 
of Philisophy in Astronomy. From July, 1973, until the present, he 
has worked at Tne Aerospace Corporation in Los Angeles, California, 
completing the research requirements for the degrees of Master of 
Science and Doctor of Philosophy in A.stronomy. In February/, 19 76, he 
began work in the Image Processing Laboratory of the Jet Propulsion 
Laboratory and became a member of the Viking Flight Team, working on 
the Viking '75 Mission to Mars. 



243 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosoohv. 



^(^X Of \n^k£^ 



A. G. Smith, Chai^mti/i 

Professor of PhysicsVazid Astronomy 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 



.P7a^ 



C. N. Olsson, Co-chairman 

Associate Professor of Physical Sciences 

and Astronomy 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 



/.ift^Uu,^- yHJ-fe-H^U- 



"■-' " 1^-HH 



S. T. Gottesman 

A.ssociate Professor of Astronomy 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 






/~\ 



G. R. Lebo 

Assistant Professor of Astronomy 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 






T. L. Bailey ,-/ 
Professor of Physids 



This dissertation was submitted to the Graduate Faculty of the Department 
of Physics and Astronomy in the College of Arts and Sciences and to the 
Graduate Council, and was accepted as partial fulfillment of the 
requirements for the degree of Doctor of Philosophy. 



March, 19 7 7 



Dean, Graduate School